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ISEE Middle Level Math : Plane Geometry

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Example Questions

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Example Question #61 : Geometry

Find the area of a triangle with a base of 17in and a height of 12in.

Possible Answers:

$121\text{in}^2$

$144\text{in}^2$

$29\text{in}^2$

$41\text{in}^2$

$102\text{in}^2$

Correct answer:

$102\text{in}^2$

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 17in. We also know the height of the triangle is 12in.

Knowing this, we can substitute into the formula. We get

$\text{area of triangle} = \frac{1}{2} \cdot 17\text{in} \cdot 12\text{in}$

$\text{area of triangle} = 17\text{in} \cdot 6\text{in}$

$\text{area of triangle} = 102\text{in}^2$

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

Find the area of a triangle with the following measurements:

Height: 13in
Base: 8in

Possible Answers:

$48\text{in}^2$

$104\text{in}^2$

$36\text{in}^2$

$96\text{in}^2$

$52\text{in}^2$

Correct answer:

$52\text{in}^2$

Explanation:

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

$A = \frac{1}{2} \cdot b \cdot h$

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

Now, we know the base is 8in. We also know the height is 13in. We can substitute into the formula. We get

$A = \frac{1}{2} \cdot 8\text{in} \cdot 13\text{in}$

$A = 4\text{in} \cdot 13\text{in}$

$A = 52\text{in}^2$

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Example Question #63 : Geometry

Find the area of a triangle with the following measurements:

base = 8in
height = 7in

Possible Answers:

$56\text{in}^2$

$24\text{in}^2$

$15\text{in}^2$

$36\text{in}^2$

$28\text{in}^2$

Correct answer:

$28\text{in}^2$

Explanation:

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

$A = \frac{1}{2} \cdot b \cdot h$

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

Now, we know the base is 8in and the height is 7in. Knowing this, we can substitute into the formula. So, we get

$A = \frac{1}{2} \cdot 8\text{in} \cdot 7\text{in}$

$A = 4\text{in} \cdot 7\text{in}$

$A = 28\text{in}^2$

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Example Question #64 : Geometry

Find the area of a triangle with a base of 5cm and a height that is two times the base.

Possible Answers:

$25\text{cm}^2$

$15\text{cm}^2$

$20\text{cm}^2$

$50\text{cm}^2$

$35\text{cm}^2$

Correct answer:

$25\text{cm}^2$

Explanation:

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

$A = \frac{1}{2} \cdot b \cdot h$

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

Now, we know the base is 5cm. We know the height is two times the base. Therefore, the height is 10cm.

So, we can substitute.

$A = \frac{1}{2} \cdot 5\text{cm} \cdot 10\text{cm}$

$A = 5\text{cm} \cdot 5\text{cm}$

$A = 25\text{cm}^2$

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Example Question #65 : Geometry

Find the area of a triangle with a base of 12in and a height of 14in.

Possible Answers:

$168\text{in}^2$

$84\text{in}^2$

$122\text{in}^2$

$40\text{in}^2$

$38\text{in}^2$

Correct answer:

$84\text{in}^2$

Explanation:

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

$A = \frac{1}{2} \cdot b \cdot h$

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

Now, we know the base of the triangle is 12in. We know the height of the triangle is 14in. So, we can substitute. We get

$A = \frac{1}{2} \cdot 12\text{in} \cdot 14\text{in}$

$A = 6\text{in} \cdot 14\text{in}$

$A = 84\text{in}^2$

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Example Question #66 : Geometry

Find the area of a triangle with a base of 8in and a height of 12in.

Possible Answers:

$36\text{in}^2$

$56\text{in}^2$

$24\text{in}^2$

$96\text{in}^2$

$48\text{in}^2$

Correct answer:

$48\text{in}^2$

Explanation:

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

$A = \frac{1}{2} \cdot b \cdot h$

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

Now, we know the base of the triangle is 8in. We also know the height is 12in. So, we can substitute. We get

$A = \frac{1}{2} \cdot 8\text{in} \cdot 12\text{in}$

$A = 4\text{in} \cdot 12\text{in}$

$A = 48\text{in}^2$

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Example Question #67 : Geometry

Find the area of a triangle with a base of 10in and a height of 11in.

Possible Answers:

$58\text{in}^2$

$21\text{in}^2$

$42\text{in}^2$

$110\text{in}^2$

$55\text{in}^2$

Correct answer:

$55\text{in}^2$

Explanation:

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

$A = \frac{1}{2} \cdot b \cdot h$

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

Now, we know the base of the triangle is 10in. We also know the height of the triangle is 11in. So, we get

$A = \frac{1}{2} \cdot 10\text{in} \cdot 11\text{in}$

$A = 5\text{in} \cdot 11\text{in}$

$A = 55\text{in}^2$

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Example Question #68 : Geometry

Find the area of a triangle with a base of 8in and a height of 12in.

Possible Answers:

$48\text{in}^2$

$72\text{in}^2$

$54\text{in}^2$

$32\text{in}^2$

$96\text{in}^2$

Correct answer:

$48\text{in}^2$

Explanation:

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

$A = \frac{1}{2} \cdot b \cdot h$

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

Now, we know the base of the triangle is 8in. We also know the height of the triangle is 12in.

Knowing this, we can substitute into the formula. We get

$A = \frac{1}{2} \cdot 8\text{in} \cdot 12\text{in}$

$A = 4\text{in} \cdot 12\text{in}$

$A = 48\text{in}^2$

Report an Error

Example Question #69 : Geometry

Find the area of a triangle with a base of $7\textup{ cm}$ and a height of $12\textup{ cm}$ .

Possible Answers:

$84\text{cm}$

$42\text{cm}$

$42\text{cm}^2$

$84\text{cm}^2$

$48\text{cm}^2$

Correct answer:

$42\text{cm}^2$

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.

We know the base is 7cm and the height is 12cm. Knowing this, we will substitute into the formula. We get

$\text{area of triangle} = \frac{1}{2} \cdot 7\text{cm} \cdot 12\text{cm}$

$\text{area of triangle} = \frac{1}{2} \cdot 84\text{cm}^2$

$\text{area of triangle} = \frac{1}{2} \cdot \frac{84\text{cm}^2}{1}$

$\text{area of triangle} = \frac{1 \cdot 84\text{cm}^2}{2 \cdot 1}$

$\text{area of triangle} = \frac{84\text{cm}^2}{2}$

$\text{area of triangle} = 42\text{cm}^2$

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Example Question #1 : How To Find Length Of A Line

Lines

Figure NOT drawn to scale.

AE = 40, AB = x, BC = x + 3, CD = 2x, DE = x-6

Evaluate .

Possible Answers:

6.2

9.6

7.2

8.6

Correct answer:

8.6

Explanation:

By the Segment Addition Postulate,

AB + BC + CD + DE = AE

x +( x + 3) +( 2x) +( x-6) = 40

5x-3 = 40

5x-3 +3 = 40 + 3

5x = 43

$5x \div 5 = 43 \div 5$

x = 8.6

AB = x = 8.6

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ISEE Middle Level Math : Plane Geometry

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #61 : Geometry

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

Example Question #63 : Geometry

Example Question #64 : Geometry

Example Question #65 : Geometry

Example Question #66 : Geometry

Example Question #67 : Geometry

Example Question #68 : Geometry

Example Question #69 : Geometry

Example Question #1 : How To Find Length Of A Line

All ISEE Middle Level Math Resources

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