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ISEE Lower Level Math : Geometry

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Example Questions

Example Question #311 : Plane Geometry

The base of a triangle is 4.4 inches, and the height of the triangle is 2.3 inches. What is the area of the triangle?

Possible Answers:

10.06 $\textup{in.}^2$

6.06 $\textup{in.}^2$

5.06 $\textup{in.}^2$

10.12 $\textup{in.}^2$

5.12 $\textup{in.}^2$

Correct answer:

5.06 $\textup{in.}^2$

Explanation:

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

4.4 * 2.3 = 10.12

10.12/2 = 5.06

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Example Question #37 : Triangles

The base of a triangle is 2.2 inches, and the height of the triangle is 1.1 inches. What is the area of the triangle?

Possible Answers:

1.21 $\textup{in.}^2$

2.42 $\textup{in.}^2$

1.42 $\textup{in.}^2$

3.42 $\textup{in.}^2$

2.40 $\textup{in.}^2$

Correct answer:

1.21 $\textup{in.}^2$

Explanation:

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

2.2 * 1.1 = 2.42

2.42/2 = 1.21

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Example Question #38 : Triangles

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

Possible Answers:

$\textup{in.}^2$

Correct answer:

$\textup{in.}^2$

Explanation:

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

5 * 8 = 40

40/2 = 20

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Example Question #39 : Triangles

Find the area of a triangle with the following measurements:

height: 9cm
base: 12cm

Possible Answers:

$54\text{cm}^2$

$84\text{cm}^2$

$108\text{cm}^2$

$72\text{cm}^2$

$36\text{cm}^2$

Correct answer:

$54\text{cm}^2$

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 of the triangle is 12in. We also know the height of the triangle is 9in.

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

$\text{area of triangle} = \frac{1}{2} \cdot 12\text{in} \cdot 9\text{in}$

$\text{area of triangle} = 6\text{in} \cdot 9\text{in}$

$\text{area of triangle} = 54\text{in}^2$

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Example Question #312 : Plane Geometry

Find the area of a triangle with a base of 6cm and a height that is two times the base.

Possible Answers:

$48\text{cm}^2$

$72\text{cm}^2$

$30\text{cm}^2$

$36\text{cm}^2$

$52\text{cm}^2$

Correct answer:

$36\text{cm}^2$

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 of the triangle is 6cm. We also know the height of the triangle is two times the base. Therefore, the height is 12cm.

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

$A = \frac{1}{2} \cdot 6\text{cm} \cdot 12\text{cm}$

$A = 3\text{cm} \cdot 12\text{cm}$

$A = 36\text{cm}^2$

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Example Question #311 : Plane Geometry

Find the area of a triangle with a base of 7in and a height that is two times the base.

Possible Answers:

$98\text{in}^2$

$56\text{in}^2$

$49\text{in}^2$

$78\text{in}^2$

$36\text{in}^2$

Correct answer:

$49\text{in}^2$

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 7in. We also know the height is two times the base. Therefore, the height is 14in.

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

$A = \frac{1}{2} \cdot 7\text{in} \cdot 14\text{in}$

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

$A = 49\text{in}^2$

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Example Question #312 : Plane Geometry

Find the area of a triangle with the following measurements:

height: 5in
base: 6in

Possible Answers:

$15\text{in}^2$

$17\text{in}^2$

$16\text{in}^2$

$11\text{in}^2$

$30\text{in}^2$

Correct answer:

$15\text{in}^2$

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 6in. We also know the height of the triangle is 5in. So, we get

$A = \frac{1}{2} \cdot 6\text{in} \cdot 5\text{in}$

$A = 3\text{in} \cdot 5\text{in}$

$A = 15\text{in}^2$

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Example Question #313 : Plane Geometry

Use the following triangle to answer the question:

Triangle5

If the triangle has a height of $9\textup{ ft}$ , find the area.

Possible Answers:

$20\textup{ ft}^2$

$21\textup{ ft}^2$

$17\textup{ ft}^2$

$26\textup{ ft}^2$

$18\textup{ ft}^2$

Correct answer:

$18\textup{ ft}^2$

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, given the triangle

Triangle5

we can see the base is 4ft. We also know it has a height of 9ft.

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

$\text{area of triangle} = \frac{1}{2} \cdot 4\text{ft} \cdot 9\text{ft}$

$\text{area of triangle} = \frac{1}{2} \cdot 36\text{ft}^2$

$\text{area of triangle} = \frac{1}{2} \cdot \frac{36\text{ft}^2}{1}$

$\text{area of triangle} = \frac{1 \cdot 36\text{ft}^2}{2 \cdot 1}$

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

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

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

The triangle below has a perimeter of $32 \textup{ cm}$ . The lengths of two sides are shown below.

What is the length of the third side?

Possible Answers:

$12 \textup{ cm}$

$23 \textup{ cm}$

$11 \textup{ cm}$

$48 \textup{ cm}$

Correct answer:

$11 \textup{ cm}$

Explanation:

Remember, the perimeter of a triangle is the sum of its three sides. First, sum up the two side lengths that we are given in the question:

$9 \textup{ cm}+12 \textup{ cm}=21 \textup{ cm}$

To find the third side, subtract the sides we know from the total perimeter:

$32 \textup{ cm}-21 \textup{ cm}=\textbf{11 \textup{cm}}$

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Example Question #2 : How To Find The Perimeter Of A Triangle

An equilateral triangle has a perimeter of $18\; in$ . How long is each side?

Possible Answers:

$3\; in$

$7\; in$

$9\; in$

$6\; in$

$8\; in$

Correct answer:

$6\; in$

Explanation:

An equilateral triangle has three congruent sides, i.e. the sides are all the same length.

The perimeter of an equilateral triangle is given by P=3s .

Thus, P=3s=18 ; then divide each side by three to get $s=6\; in$ .

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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 : Plane Geometry

Example Question #37 : Triangles

Example Question #38 : Triangles

Example Question #39 : Triangles

Example Question #312 : Plane Geometry

Example Question #311 : Plane Geometry

Example Question #312 : Plane Geometry

Example Question #313 : Plane Geometry

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

Example Question #2 : How To Find The Perimeter Of A Triangle

All ISEE Lower Level Math Resources

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