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 #3 : Geometry

What is the area of a triangle with a base of 22 cm and a height of 9 cm?

Possible Answers:

$45\ cm^{2}$

$99\ cm^{2}$

$198\ cm^{2}$

$98\ cm^{2}$

Correct answer:

$99\ cm^{2}$

Explanation:

Use the area of a triangle formula

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

Plug in the base and height. This gives you $99\ cm^{2}$ .

Report an Error

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

Right Triangle A has hypotenuse 25 inches and one leg of length 24 inches; Right Triangle B has hypotenuse 15 inches and one leg of length 9 inches; Rectangle C has length 16 inches. The area of Rectangle C is the sum of the areas of the two right triangles. What is the width of Rectangle C?

Possible Answers:

$17 \frac{1}{4} \textrm{ in}$

$6 \frac{7}{8} \textrm{ in}$

$10 \frac{1}{2} \textrm{ in}$

$8 \frac{5}{8} \textrm{ in}$

$14\frac{7}{8} \textrm{ in}$

Correct answer:

$8 \frac{5}{8} \textrm{ in}$

Explanation:

The area of a right triangle is half the product of its legs. In each case, we know the length of one leg and the hypotenuse, so we need to apply the Pythagorean Theorem to find the second leg, then take half the product of the legs:

Right Triangle A:

The length of the second leg is

$\sqrt{25^{2} -24 ^{2}} = \sqrt{625 - 576} = \sqrt{49} = 7$ inches.

The area is

$\frac{1}{2} \times 7 \times 24 = 84$ square inches.

Right Triangle B:

The length of the second leg is

$\sqrt{15^{2} -9 ^{2}} = \sqrt{225 - 81} = \sqrt{144} = 12$ inches.

The area is

$\frac{1}{2} \times 9 \times 12 = 54$ square inches.

The sum of the areas is 84 + 54 = 138 square inches.

The area of a rectangle is the product of its length and its height. Therefore, the height is the quotient of the area and the length, which, for Rectangle C, is $138 \div 16 = 8 \frac{5}{8}$ inches.

Report an Error

Example Question #4 : Geometry

Right Triangle A has legs of lengths 10 inches and 14 inches; Right Triangle B has legs of length 20 inches and 13 inches; Rectangle C has length 30 inches. The area of Rectangle C is the sum of the areas of the two right triangles. What is the height of Rectangle C?

Possible Answers:

Insufficient information is given to determine the height.

$6 \frac{2}{3} \textrm{ in}$

$10 \textrm{ in}$

$13\frac{1}{3} \textrm{ in}$

$5 \textrm{ in}$

Correct answer:

$6 \frac{2}{3} \textrm{ in}$

Explanation:

The area of a right triangle is half the product of its legs. The area of Right Triangle A is equal to $\frac{1}{2} \times 10 \times 14 = 70$ square inches; that of Right Triangle B is equal to $\frac{1}{2} \times 20 \times 13 = 130$ square inches. The sum of the areas is 70 + 130 = 200 square inches, which is the area of Rectangle C.

The area of a rectangle is the product of its length and its height. Therefore, the height is the quotient of the area and the length, which, for Rectangle C, is $200 \div 30 = 6 \frac{2}{3}$ inches.

Report an Error

Example Question #5 : Geometry

Heron

Give the area of the above triangle.

Possible Answers:

1,125

450

900

800

675

Correct answer:

900

Explanation:

By Heron's formula, the area of a triangle given its sidelengths is

$A =\sqrt{ s (s-a) (s-b) (s-c)}$

Where a, b, c are the sidelengths and

$s = \frac{1}{2} (a+b+c)$ ,

or half the perimeter.

Setting a = 50, b = 45, c=85 ,

$s = \frac{1}{2} (a+b+c) = \frac{1}{2} (50+45+85) = 90$

Therefore,

$A =\sqrt{ s (s-a) (s-b) (s-c)}$

$A =\sqrt{90 (90 -50) (90 -45) (90 -85)}$

$A =\sqrt{90 \cdot 40 \cdot 45 \cdot 5 }$

$A =\sqrt{810,000 }$

A =900

Report an Error

Example Question #6 : Geometry

Heron

Give the area of the above triangle.

Possible Answers:

$60 \sqrt{7 }$

$30 \sqrt{ 14 }$

216

240

160

Correct answer:

$60 \sqrt{7 }$

Explanation:

By Heron's formula, the area of a triangle given its sidelengths is

$A =\sqrt{ s (s-a) (s-b) (s-c)}$ ,

where a, b, c are the sidelengths and

$s = \frac{1}{2} (a+b+c)$ ,

or half the perimeter.

Setting a = 16, b = 20, c=24 ,

$s = \frac{1}{2} (a+b+c) = \frac{1}{2} (16+20+24) = 30$ .

Therefore,

$A =\sqrt{ s (s-a) (s-b) (s-c)}$

$A =\sqrt{ 30 (30-16) (30-20) (30-24)}$

$A =\sqrt{ 30 \cdot 14 \cdot 10 \cdot 6 }$

$A = \sqrt{25,200 }$

$A = \sqrt{3,600 } \cdot\sqrt{7}$

$A = 60 \sqrt{7 }$

Report an Error

Example Question #1781 : Hspt Mathematics

Find the area of the following parallelogram:

Note: The formula for the area of a parallelogram is $A=b\times h$ .

Possible Answers:

$32\: in^2$

$50\: in^2$

$30\: in^2$

$60\: in^2$

Correct answer:

$50\: in^2$

Explanation:

The base of the parallelogram is 10, while the height is 5.

$A=b\times h$

$A=10\times5=50\: in^2$

Report an Error

Example Question #1 : Parallelograms

Find the area:

Question_5

Possible Answers:

$\small 24$

$\small 12$

$\small 16$

$\small 32$

Correct answer:

$\small 24$

Explanation:

The area of a parallelogram can be determined using the following equation:

$\small A=bh$

Therefore,

$\small A=8\times3=24$

Report an Error

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

What is the area of a rectangle with length $14\ cm$ and width $12\ cm$ ?

Possible Answers:

$144\; cm^{2}$

$158\;cm^{2}$

$168\;cm^{2}$

$148\; cm^{2}$

$198\;cm^{2}$

Correct answer:

$168\;cm^{2}$

Explanation:

The formula for the area, , of a rectangle when we are given its length, , and width, , is A = L * W .

To calculate this area, just multiply the two terms.

$A = 14\ cm * 12\ cm = 168\; cm^{2}$

Report an Error

Example Question #11 : Geometry

Order the following from least area to greatest area:

Figure A: A rectangle with length 10 inches and width 14 inches.

Figure B: A square with side length 1 foot.

Figure C: A triangle with base 16 inches and height 20 inches.

Possible Answers:

A, C, B

A, B, C

C,A, B

B, A, C

B, C, A

Correct answer:

A, B, C

Explanation:

Figure A has area $10 \times 14 = 140$ square inches.

Figure B has area $12 \times 12 = 144$ square inches, 1 foot being equal to 12 inches.

Figure C has area $\frac{1}{2} \times 16 \times 20 = 160$ square inches.

The figures, arranged from least area to greatest, are A, B, C.

Report an Error

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

Prism

Give the surface area of the above box in square inches.

Possible Answers:

$672 \textrm{ in}^{2}$

$1,344 \textrm{ in}^{2}$

$3,168 \textrm{ in}^{2}$

$816 \textrm{ in}^{2}$

$1,056\textrm{ in}^{2}$

Correct answer:

$1,344 \textrm{ in}^{2}$

Explanation:

Use the surface area formula, substituting L = 22, W = H = 12 :

A = 2LW + 2LH + 2WH

$A = 2 \cdot 22 \cdot 12 + 2 \cdot 22 \cdot 12 + 2\cdot 12\cdot 12$

A = 528 + 528 + 288

A =1,344 square inches

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

Spanish Tutors in Philadelphia, ACT Tutors in Atlanta, GRE Tutors in Houston, Reading Tutors in Denver, French Tutors in Boston, Physics Tutors in Atlanta, SSAT Tutors in Seattle, Algebra Tutors in Phoenix, Reading Tutors in Philadelphia, Algebra Tutors in New York City

Popular Courses & Classes

Spanish Courses & Classes in San Francisco-Bay Area, SSAT Courses & Classes in Atlanta, ACT Courses & Classes in Los Angeles, ISEE Courses & Classes in Philadelphia, GRE Courses & Classes in Washington DC, GMAT Courses & Classes in Miami, ISEE Courses & Classes in Boston, GRE Courses & Classes in San Diego, ISEE Courses & Classes in San Diego, ISEE Courses & Classes in San Francisco-Bay Area

Popular Test Prep

LSAT Test Prep in San Francisco-Bay Area, ACT Test Prep in Los Angeles, GRE Test Prep in Dallas Fort Worth, ISEE Test Prep in San Diego, GMAT Test Prep in Atlanta, SSAT Test Prep in Phoenix, SAT Test Prep in Boston, LSAT Test Prep in Los Angeles, GRE Test Prep in San Diego, MCAT Test Prep in Chicago

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 #3 : Geometry

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

Example Question #4 : Geometry

Example Question #5 : Geometry

Example Question #6 : Geometry

Example Question #1781 : Hspt Mathematics

Example Question #1 : Parallelograms

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

Example Question #11 : Geometry

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

All HSPT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: