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HSPT Math : Geometry

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Example Question #1943 : Isee Middle Level (Grades 7 8) Mathematics Achievement

What is the area of a square with a side length of 4?

Possible Answers:

Correct answer:

Explanation:

The area of a square is represented by the equation $\dpi{100} Area = side^{2}$ .

Therefore the area of this square is $\dpi{100} 4^{2}=16$ .

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Example Question #1944 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Square A has sides measuring 5 meters. A second square, Square B, has sides that are 2 meters longer than the sides of Square A. What is the difference in area of Square A and Square B?

Possible Answers:

$8\ m^2$

$9\ m^2$

$21\ m^2$

$24\ m^{2}$

$49\ m^2$

Correct answer:

$24\ m^{2}$

Explanation:

The area of Square A is 5 * 5, or 25 m².

Since each of Square B's sides is 2 meters longer, the sides measure 7 meters. Therefore, the area of square B is 49 m².

Subtract to find the difference in areas: $49-25=24\ m^2$

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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:

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

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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.

$s=\sqrt{3}$

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

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

Trapezoid

What is the area of the above trapezoid?

Possible Answers:

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

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

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

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

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

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

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

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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

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Example Question #212 : Geometry

Trapezoid

What is the area of the trapezoid?

Possible Answers:

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

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

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

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

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

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.

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

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

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

Possible Answers:

$\small 190$

$\small 93$

$\small 48$

$\small 95$

$\small 47$

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 $\small 95$ .

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

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:

$y = 24\textrm{ in}$

$y = 16 \textrm{ in}$

$y = 26 \textrm{ in}$

$y = 32 \textrm{ in}$

$y = 20 \textrm{ in}$

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

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

$y = 16 \textrm{ in}$

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Example Question #4 : Area Of A Triangle

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

What is the area of this shape?

Possible Answers:

$25\ in^{2}$

$40\ in^{2}$

$21\ in^{2}$

$15\ in^{2}$

$32.5\ in^{2}$

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.

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HSPT Math : Geometry

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #1943 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #1944 : Isee Middle Level (Grades 7 8) Mathematics Achievement

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 #212 : Geometry

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

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

Example Question #4 : Area Of A Triangle

All HSPT Math Resources

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