We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

Create An Account

All HSPT Math Resources

6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #5 : How To Find The Area Of A Square

The ratio of the length of a side of one square to the length of the side of another square is $\frac{a}{b}$ . Give the ratio of the area of the second square to the area of the first square.

Possible Answers:

$\frac{b^2}{a}$

$\frac{a^2}{b^2}$

$\frac{b^2}{a^2}$

$\frac{b}{a^2}$

Correct answer:

$\frac{b^2}{a^2}$

Explanation:

The area of a square can be found as follows:

Area=x^2

Where:

$x=Side\ Length$

So we can write:

$\frac{Area\ 2}{Area\ 1}=\frac{b^2}{a^2}$

Report an Error

Example Question #6 : How To Find The Area Of A Square

What is the area of a square if the length of one side is $\sqrt{3}$ ?

Possible Answers:

$\frac{1}{3}$

$3\sqrt{3}$

$\sqrt{3}$

Correct answer:

Explanation:

The area of a square is found by multiplying one side by itself.

$A=s\times s=s^2$

We are given the side length, allowing us to solve.

$s=\sqrt{3}$

$A=(\sqrt{3})^2=3$

Report an Error

Example Question #1 : How To Find The Area Of A Trapezoid

Trapezoid

What is the area of the above trapezoid?

Possible Answers:

$142.04\textrm{ m}^{2}$

$96.48\textrm{ m}^{2}$

$218.36\textrm{ m}^{2}$

$76.32\textrm{ m}^{2}$

$109.18\textrm{ m}^{2}$

Correct answer:

$109.18\textrm{ m}^{2}$

Explanation:

To find the area of a trapezoid, multiply one half (or 0.5, since we are working with decimals) by the sum of the lengths of its bases (the parallel sides) by its height (the perpendicular distance between the bases). This quantity is

$A = 0.5 \cdot (7.2 + 13.4) \cdot 10.6 =0.5 \cdot 20.6 \cdot 10.6 = 109.18\textrm{ m}^{2}$

Report an Error

Example Question #1 : How To Find The Area Of A Trapezoid

Find the area of the trapezoid:

Question_7

Possible Answers:

Correct answer:

Explanation:

The area of a trapezoid can be determined using the equation $A=\frac{1}{2}(b_1+b_2)h$ .

$A=\frac{1}{2}(6+8)(4)$

$A=\frac{1}{2}(14)(4)$

A=(7)(4)=28

Report an Error

Example Question #2 : How To Find The Area Of A Trapezoid

Trapezoid

What is the area of the trapezoid?

Possible Answers:

$135\textrm{ m}^{2}$

$99\textrm{ m}^{2}$

$105\textrm{ m}^{2}$

$63\textrm{ m}^{2}$

$198\textrm{ m}^{2}$

Correct answer:

$99\textrm{ m}^{2}$

Explanation:

To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.

$A = \frac{1}{2} \cdot (7 + 15) \cdot 9 = \frac{1}{2} \cdot 22 \cdot 9 = 99 \textrm{ m}^2$

Report an Error

Example Question #31 : Geometry

A triangle has a base of $\small 43$ and an area of $\small 2042.5$ . What is the height?

Possible Answers:

$\small 47$

$\small 48$

$\small 95$

$\small 93$

$\small 190$

Correct answer:

$\small 95$

Explanation:

The area of a triangle is found by multiplying the base by the height and dividing by two:

$\small \frac{b\cdot h}{2}$

In this problem we are given the base, which is $\small 43$ , and the area, which is $\small 2042.5$ . First we write an equation using $\small h$ as our variable.

$\small \frac{43\cdot h}{2}=2042.5$

To solve this equation, first multply both sides by $\small 2$ , becuase multiplication is the opposite of division and therefore allows us to eliminate the $\small 2$ .

The left-hand side simplifies to:

$\small \frac{43\cdot h}{2}\cdot 2=43\cdot h$

The right-hand side simplifies to:

$\small 2042.5\cdot 2=4085$

So our equation is now:

$\small \small 43\cdot h=4085$

Next we divide both sides by $\small \small 43$ , because division is the opposite of multiplication, so it allows us to isolate the variable by eliminating $\small \small 43$ .

$\small \frac{43\cdot h}{43}= h$

$\small \frac{4085}{43}=95$

$\small h=95$

So the height of the triangle is $\small 95$ .

Report an Error

Example Question #33 : Geometry

Triangle

Note: Figure NOT drawn to scale.

The above triangle has area 36 square inches. If $x = 4.5 \textrm{ in}$ , then what is ?

Possible Answers:

$y = 16 \textrm{ in}$

$y = 26 \textrm{ in}$

$y = 20 \textrm{ in}$

$y = 32 \textrm{ in}$

$y = 24\textrm{ in}$

Correct answer:

$y = 16 \textrm{ in}$

Explanation:

The area of a triangle is one half the product of its base and its height - in the above diagram, that means

$A = \frac{1}{2}xy$ .

Substitute A = 36, x = 4.5 , and solve for .

$\frac{1}{2} \cdot 4.5 \cdot y = 36$

2.25 y = 36

$2.25 y \div 2.25= 36\div 2.25$

$y = 16 \textrm{ in}$

Report an Error

Example Question #6 : How To Find The Area Of A Triangle

Please use the following shape for the question. 5x3-adams-graphoc

What is the area of this shape?

Possible Answers:

$40\ in^{2}$

$32.5\ in^{2}$

$21\ in^{2}$

$15\ in^{2}$

$25\ in^{2}$

Correct answer:

$32.5\ in^{2}$

Explanation:

From this shape we are able to see that we have a square and a triangle, so lets split it into the two shapes to solve the problem. We know we have a square based on the 90 degree angles placed in the four corners of our quadrilateral.

Since we know the first part of our shape is a square, to find the area of the square we just need to take the length and multiply it by the width. Squares have equilateral sides so we just take 5 times 5, which gives us 25 inches squared.

We now know the area of the square portion of our shape. Next we need to find the area of our right triangle. Since we know that the shape below the triangle is square, we are able to know the base of the triangle as being 5 inches, because that base is a part of the square's side.

To find the area of the triangle we must take the base, which in this case is 5 inches, and multipy it by the height, then divide by 2. The height is 3 inches, so 5 times 3 is 15. Then, 15 divided by 2 is 7.5.

We now know both the area of the square and the triangle portions of our shape. The square is 25 inches squared and the triangle is 7.5 inches squared. All that is remaining is to added the areas to find the total area. Doing this gives us 32.5 inches squared.

Report an Error

Example Question #2 : Area Of A Triangle

What is the area of the triangle?

Question_11

Possible Answers:

$\small 70$

$\small 84$

$\small 42$

$\small 35$

Correct answer:

$\small 35$

Explanation:

Area of a triangle can be determined using the equation:

$\small A=\frac{1}{2}bh$

$\small A=\frac{1}{2}(14)(5)=35$

Report an Error

Example Question #1 : How To Find The Area Of A Triangle

Bill paints a triangle on his wall that has a base parallel to the ground that runs from one end of the wall to the other. If the base of the wall is 8 feet, and the triangle covers 40 square feet of wall, what is the height of the triangle?

Possible Answers:

$8\: feet$

$10\: feet$

$9\: feet$

$11\: feet$

$20\: feet$

Correct answer:

$10\: feet$

Explanation:

In order to find the area of a triangle, we multiply the base by the height, and then divide by 2.

$\small \frac{b\cdot h}{2}$

In this problem we are given the base and the area, which allows us to write an equation using $\small h$ as our variable.

$\small \frac{8\cdot h}{2}=40$

Multiply both sides by two, which allows us to eliminate the two from the left side of our fraction.

The left-hand side simplifies to:

$\small \frac{8\cdot h}{2}\cdot 2=8\cdot h$

The right-hand side simplifies to:

$\small 40\cdot 2=80$

Now our equation can be rewritten as:

$\small 8\cdot h=80$

Next we divide by 8 on both sides to isolate the variable:

$\small \frac{8\cdot h}{8}=h$

$\small \frac{80}{8}=10$

$\small h=10$

Therefore, the height of the triangle is $\small 10 \: feet$ .

Report an Error

View Tutors

Crystal
Certified Tutor

SUNY at Binghamton, Bachelor of Science, Mechanical Engineering.

View Tutors

Kara
Certified Tutor

University of Central Missouri, Bachelor of Science, Science Teacher Education. University of Central Missouri, Certificate, ...

View Tutors

Eva
Certified Tutor

Technicka Univerzita Liberec, Bachelor of Education, Education.

All HSPT Math Resources

6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Calculus Tutors in Miami, SAT Tutors in New York City, GRE Tutors in New York City, LSAT Tutors in Houston, Physics Tutors in Seattle, Chemistry Tutors in Seattle, GRE Tutors in Dallas Fort Worth, Spanish Tutors in San Francisco-Bay Area, Calculus Tutors in San Diego, Biology Tutors in Houston

Popular Courses & Classes

GMAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Dallas Fort Worth, LSAT Courses & Classes in Miami, Spanish Courses & Classes in San Francisco-Bay Area, ISEE Courses & Classes in Boston, LSAT Courses & Classes in Houston, GRE Courses & Classes in Washington DC, LSAT Courses & Classes in Boston, SSAT Courses & Classes in Miami, SAT Courses & Classes in Philadelphia

Popular Test Prep

LSAT Test Prep in Phoenix, ISEE Test Prep in Boston, GRE Test Prep in Seattle, ISEE Test Prep in Dallas Fort Worth, GRE Test Prep in Phoenix, SSAT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Washington DC, GRE Test Prep in Los Angeles, MCAT Test Prep in Miami, GMAT Test Prep in Atlanta

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #5 : How To Find The Area Of A Square

Example Question #6 : How To Find The Area Of A Square

Example Question #1 : How To Find The Area Of A Trapezoid

Example Question #1 : How To Find The Area Of A Trapezoid

Example Question #2 : How To Find The Area Of A Trapezoid

Example Question #31 : Geometry

Example Question #33 : Geometry

Example Question #6 : How To Find The Area Of A Triangle

Example Question #2 : Area Of A Triangle

Example Question #1 : How To Find The Area Of A Triangle

All HSPT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: