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ISEE Lower Level Math : Geometry

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Example Questions

Example Question #311 : Geometry

If you have a right triangle with a height of 6 inches, a base of 8 inches, and a hypotenuse of 10 inches, what is its area?

Possible Answers:

140in^2

240in^2

40in^2

24in^2

Correct answer:

24in^2

Explanation:

If you have a right triangle with a height of 6 inches, a base of 8 inches, and a hypotenuse of 10 inches, what is its area?

To find area of a triangle, we use

$A_{triangle}=\frac{1}{2}bh$

So, plug in our base and height measurements to get our answer:

$A_{triangle}=\frac{1}{2}*8in*6in=24 in^2$

Coincidentally, the same as our perimeter

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Example Question #12 : How To Find The Area Of A Triangle

How much area does a triangular garden have with a base of and a height of ?

Possible Answers:

Correct answer:

Explanation:

The area of a triangle is

$\frac{1}{2}*base*height$

so given that the base is 5 and the height is 6, the area equation becomes,

5*6=30

and

$\frac{1}{2}*30=15$ .

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Example Question #18 : How To Find The Area Of A Triangle

7769e6365587d735d2ecf55b347a7f06a0cd32eb

If the formula for the area of a triangle is

$A=\frac{1}{2} \times base \times height$ ,

what is the area of this triangle?

Possible Answers:

$10cm^{^2{}}$

$40cm^{2}$

$20cm^{2_{}}$

$13cm^{2}$

Correct answer:

$20cm^{2_{}}$

Explanation:

Using the formula:

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

where

b=8, h=5

7769e6365587d735d2ecf55b347a7f06a0cd32eb

$A=\frac{1}{2}(8\times 5)$

Since $8\times 5=40$ the equation becomes

$A=\frac{1}{2}(40)=\frac{40}{2}=\frac{20\cdot 2}{2}=20$

$A= 20cm^{2}$

Note: Answer will always be represented with the measurement to the second power when calculating the area of a triangle.

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Example Question #19 : How To Find The Area Of A Triangle

Find the area of a triangle with a height of 12in and a base that is half the height.

Possible Answers:

$72\text{in}$

$36\text{in}^2$

$72\text{in}^2$

$18\text{in}$

$36\text{in}$

Correct answer:

$36\text{in}^2$

Explanation:

The formula to find the area of a triangle is

$\text{area of triangle} = \frac{1}{2} \cdot b \cdot h$

where b is the base and h is the height of the triangle.

We know the height of the triangle is 12in. We know the base is half the height, so the base is 6in. Now, we can substitute. We get

$\text{area of triangle} = \frac{1}{2} \cdot 6\text{in} \cdot 12\text{in}$

$\text{area of triangle} = \frac{1}{2} \cdot72\text{in}^2$

$\text{area of triangle} = 36\text{in}^2$

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Example Question #11 : How To Find The Area Of A Triangle

The base of a triangle is inches, and the height of the triangle is inches. What is the area of the triangle?

Possible Answers:

y/2

.5y

Correct answer:

Explanation:

To find the area of a triangle, multiply the base by the height, and divide by two. The best answer is:

y * 2 = 2y

2y/2 = y

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Example Question #21 : How To Find The Area Of A Triangle

The base of a triangle is 4.5 inches, and the height of the triangle is inches. What is the area of the triangle?

Possible Answers:

Correct answer:

Explanation:

To find the area of a triangle, multiply the base by the height, and divide by two. The best answer is:

4.5 * 4 = 18

18/2 = 9

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Example Question #21 : How To Find The Area Of A Triangle

The base of a triangle is inches, and the height of the triangle is inches. What is the area of the triangle?

Possible Answers:

Correct answer:

Explanation:

To find the area of a triangle, multiply the base by the height, and divide by two. The best answer is:

3 * 4 = 12

12/2 = 6

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Example Question #311 : Geometry

The base of a triangle is inches, and the height of the triangle is x + 2 inches. What is the area of the triangle?

Possible Answers:

x^2 + x

x^2 + 2x

$\frac{x^2 + 2x}{2}$

$\frac{x^2 + x}{2}$

$\frac{2x^2 + 2x}{2}$

Correct answer:

$\frac{x^2 + 2x}{2}$

Explanation:

To find the area of a triangle, multiply the base by the height, and divide by two. The best answer is:

First multiply the base and the height together:

x(x+2) = x^2 + 2x

Then divide the product by two:

$\frac{x^2 + 2x}{2}$

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Example Question #22 : How To Find The Area Of A Triangle

Find the area of a triangle with a base of length 12cm and a height that is half the base.

Possible Answers:

$36\text{cm}^2$

$18\text{cm}^2$

$72\text{cm}$

$36\text{cm}$

$72\text{cm}^2$

Correct answer:

$36\text{cm}^2$

Explanation:

To find the area of a triangle, we will use the following formula:

$\text{area of triangle} = \frac{1}{2} \cdot b \cdot h$

where b is the base and h is the height of the triangle.

Now, we know the base is 12cm. We also know that the height is half the base. Therefore, the height is 6cm. Knowing this, we can substitute into the formula. We get

$\text{area of triangle} = \frac{1}{2} \cdot 12\text{cm} \cdot 6\text{cm}$

$\text{area of triangle} = \frac{1}{2} \cdot 72\text{cm}^2$

$\text{area of triangle} = \frac{1}{2} \cdot \frac{72\text{cm}^2}{1}$

$\text{area of triangle} = \frac{1 \cdot 72\text{cm}^2}{2 \cdot 1}$

$\text{area of triangle} = \frac{72\text{cm}^2}{2}$

$\text{area of triangle} = 36\text{cm}^2$

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Example Question #312 : Geometry

Find the area of a triangle with a base of 3 feet and a height that is two times the base.

Possible Answers:

$9\text{ft}^2$

$18\text{ft}^2$

$9\text{ft}$

$18\text{ft}$

$15\text{ft}$

Correct answer:

$9\text{ft}^2$

Explanation:

To find the area of a triangle, we will use the following formula:

$\text{area of triangle} = \frac{1}{2} \cdot b \cdot h$

where b is the base and h is the height of the triangle.

Now, we know the base of the triangle is 3 feet. We also know the height of the triangle is two times the base. Therefore, the height is 6 feet. Knowing all of this, we can substitute into the formula. We get

$\text{area of triangle} = \frac{1}{2} \cdot 3\text{ft} \cdot 6\text{ft}$

$\text{area of triangle} = \frac{1}{2} \cdot 18\text{ft}^2$

$\text{area of triangle} = \frac{1}{2} \cdot \frac{18\text{ft}^2}{1}$

$\text{area of triangle} = \frac{1 \cdot 18\text{ft}^2}{2 \cdot 1}$

$\text{area of triangle} = \frac{18\text{ft}^2}{2}$

$\text{area of triangle} = 9\text{ft}^2$

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ISEE Lower Level Math : Geometry

Study concepts, example questions & explanations for ISEE Lower Level Math

All ISEE Lower Level Math Resources

Example Questions

Example Question #311 : Geometry

Example Question #12 : How To Find The Area Of A Triangle

Example Question #18 : How To Find The Area Of A Triangle

Example Question #19 : How To Find The Area Of A Triangle

Example Question #11 : How To Find The Area Of A Triangle

Example Question #21 : How To Find The Area Of A Triangle

Example Question #21 : How To Find The Area Of A Triangle

Example Question #311 : Geometry

Example Question #22 : How To Find The Area Of A Triangle

Example Question #312 : Geometry

All ISEE Lower Level Math Resources

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