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ISEE Middle Level Math : Plane Geometry

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Example Question #51 : Geometry

Right triangle 3

Give the area of the above triangle.

Possible Answers:

750

812 .5

1,500

1,625

Correct answer:

750

Explanation:

The area of a right triangle is half the product of the lengths of its legs, which here are 25 and 60. So

$A = \frac{1}{2} \cdot 25 \cdot 60 = 750$

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Example Question #52 : Triangles

Find the area of a triangle with a base of 10cm and a height that is half the base.

Possible Answers:

$50\text{cm}^2$

$50\text{cm}$

$25\text{cm}^2$

$25\text{cm}$

$20\text{cm}$

Correct answer:

$25\text{cm}^2$

Explanation:

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

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

Now, we know the base has a length of 10cm. We also know the height is half the base. Therefore, the height is 5cm. Knowing this, we can substitute into the formula. We get

$\text{area of triangle} = \frac{1}{2} \cdot 10\text{cm} \cdot 5\text{cm}$

$\text{area of triangle} = \frac{1}{2} \cdot 50\text{cm}^2$

$\text{area of triangle} = 25\text{cm}^2$

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Example Question #53 : Triangles

The roof of a skyscraper forms a right triangle with equal arms of length 50 meters. Find the area of the roof of the skyscraper.

Possible Answers:

250m^2

2500m^2

125m^2

1250m^2

Correct answer:

1250m^2

Explanation:

The roof of a skyscraper forms a right triangle with equal arms of length 50 meters. Find the area of the roof of the skyscraper.

To find the area of a triangle, use the following:

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

Where b and h are the base and height.

In this case, we are told that the base and height are both 50 meters, thus, the perimeter will be:

$A_{triangle}=\frac{1}{2}50m*50m=\frac{1}{2}*2500m^2=1250m^2$

So our answer is:

1250m^2

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Example Question #54 : Triangles

Your neighbor is building a sandbox out of two by fours. The sandbox will be in the shape of a right triangle, with the legs being 12 feet and 16 feet. What will the area of the sandbox be?

Possible Answers:

108ft^2

96 ft^2

192ft^2

48ft^2

Correct answer:

96 ft^2

Explanation:

Your neighbor is building a sandbox out of two by fours. The sandbox will be in the shape of a right triangle, with the legs being 12 feet and 16 feet. What will the area of the sandbox be?

The are of a triangle is found as follows:

$A_{triangle}=\frac{1}{2}b*h$

Where b is the length of the base and h is the length of the height.

We are told two lengths of our triangle, and because it is a right triangle, we can use them as base and height. Note that it doesn't really matter which one is which.

$A=\frac{1}{2}*12ft*16ft=6ft*16ft=96ft^2$

Because this is an area question, our units must be squared.

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Example Question #51 : Triangles

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

Possible Answers:

$72\text{ft}^2$

$36\text{ft}^2$

$36\text{ft}$

$12\text{ft}^2$

$72\text{ft}$

Correct answer:

$36\text{ft}^2$

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 has a length of 6 feet. We also know the height is two times the base. Therefore, the height is 12 feet. Knowing this, we can substitute into the formula. We get

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

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

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

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

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

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

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Example Question #56 : Triangles

Find the area of a triangle with a base of 7cm and a height of 12cm.

Possible Answers:

$84\text{cm}$

$42\text{cm}^2$

$84\text{cm}^2$

$48\text{cm}^2$

$42\text{cm}$

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 #57 : Triangles

Find the area of a triangle with a base of 6 feet and a height that is twice the base.

Possible Answers:

$42\text{ft}^2$

$72\text{ft}^2$

$18\text{ft}^2$

$12\text{ft}^2$

$36\text{ft}^2$

Correct answer:

$36\text{ft}^2$

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 is 6ft. We also know the height is twice (or two times) the base. Therefore, the height is 12ft.

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

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

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

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

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

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

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

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Example Question #58 : Triangles

Find the area of a triangle with a base of 6cm and a height of 18cm.

Possible Answers:

$54\text{cm}$

$108\text{cm}$

$54\text{cm}^2$

$42\text{cm}^2$

$108\text{cm}^2$

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 6cm. We also know the height of the triangle is 18cm.

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

$\text{area of triangle} = \frac{1}{2} \cdot 6\text{cm} \cdot 18\text{cm}$

$\text{area of triangle} = \frac{1}{2} \cdot 108\text{cm}^2$

$\text{area of triangle} = \frac{1}{2} \cdot \frac{108\text{cm}^2}{1}$

$\text{area of triangle} = \frac{1 \cdot 108\text{cm}^2}{2 \cdot 1}$

$\text{area of triangle} = \frac{108\text{cm}^2}{2}$

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

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Example Question #59 : Triangles

Use the following image to answer the question:

Triangle6

Find the area of the triangle if it has a height of 11 feet.

Possible Answers:

$66\text{ft}^2$

$60\text{ft}^2$

$72\text{ft}^2$

$39\text{ft}^2$

$33\text{ft}^2$

Correct answer:

$33\text{ft}^2$

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, let's look at the triangle.

Triangle6

We can see it has a base of 6 feet. We also know it has a height of 11 feet.

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

$\text{area of triangle} = \frac{1}{2} \cdot 6\text{ft} \cdot 11\text{ft}$

$\text{area of triangle} = \frac{1}{2} \cdot 66\text{ft}^2$

$\text{area of triangle} = \frac{1}{2} \cdot \frac{66\text{ft}^2}{1}$

$\text{area of triangle} = \frac{1 \cdot 66\text{ft}^2}{2 \cdot 1}$

$\text{area of triangle} = \frac{66\text{ft}^2}{2}$

$\text{area of triangle} = 33\text{ft}^2$

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Example Question #60 : Triangles

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

Possible Answers:

$72\text{ft}^2$

$18\text{ft}^2$

$36\text{ft}^2$

$24\text{ft}^2$

$6\text{ft}^2$

Correct answer:

$36\text{ft}^2$

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 height of the triangle is 12 feet. We also know the base is half the height. Therefore, the base is 6 feet.

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

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

$\text{area of triangle} = 3\text{ft} \cdot 12\text{ft}$

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

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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 #51 : Geometry

Example Question #52 : Triangles

Example Question #53 : Triangles

Example Question #54 : Triangles

Example Question #51 : Triangles

Example Question #56 : Triangles

Example Question #57 : Triangles

Example Question #58 : Triangles

Example Question #59 : Triangles

Example Question #60 : Triangles

All ISEE Middle Level Math Resources

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