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ISEE Lower Level Quantitative : Geometry

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

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All ISEE Lower Level Quantitative Resources

20 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #741 : Geometry

What is the area of the right triangle in the following figure?

Possible Answers:

$64\textup{ in}^2$

$62.5\textup{ in}^2$

$66\textup{ in}^2$

$58.5\textup{ in}^2$

$60\textup{ in}^2$

Correct answer:

$64\textup{ in}^2$

Explanation:

There are several different ways to solve for the area of a right triangle. In this lesson, we will transform the right triangle into a rectangle, use the the simpler formula for area of a rectangle to solve for the new figure's area, and divide this area in half in order to solve for the area of the original figure.

First, let's transform the triangle into a rectangle:

4 4

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=16\times 8$

A=128

Last, notice that our triangle is exactly half the size of the rectangle that we made. This means that in order to solve for the area of the triangle we will need to take half of the area of the rectangle, or divide it by .

$128\div 2= 64\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

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Example Question #742 : Geometry

What is the area of the right triangle in the following figure?

Possible Answers:

$105.5\textup{ in}^2$

$104\textup{ in}^2$

$101.5\textup{ in}^2$

$102\textup{ in}^2$

$100\textup{ in}^2$

Correct answer:

$102\textup{ in}^2$

Explanation:

First, let's transform the triangle into a rectangle:

1 1

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=17\times 12$

A=204

$204\div 2= 102\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

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Example Question #743 : Geometry

What is the area of the right triangle in the following figure?

Possible Answers:

$95\textup{ in}^2$

$91.5\textup{ in}^2$

$96\textup{ in}^2$

$90.5\textup{ in}^2$

$93.5\textup{ in}^2$

Correct answer:

$93.5\textup{ in}^2$

Explanation:

First, let's transform the triangle into a rectangle:

2 2

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=17\times 11$

A=187

$187\div 2= 93.5\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

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Example Question #744 : Geometry

What is the area of the right triangle in the following figure?

Possible Answers:

$87.5\textup{ in}^2$

$81\textup{ in}^2$

$83.5\textup{ in}^2$

$89\textup{ in}^2$

$85\textup{ in}^2$

Correct answer:

$85\textup{ in}^2$

Explanation:

First, let's transform the triangle into a rectangle:

3 3

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=17\times 10$

A=170

$170\div 2= 85\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

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Example Question #745 : Geometry

What is the area of the right triangle in the following figure?

Possible Answers:

$76.5\textup{ in}^2$

$80\textup{ in}^2$

$78.5\textup{ in}^2$

$72.5\textup{ in}^2$

$74\textup{ in}^2$

Correct answer:

$76.5\textup{ in}^2$

Explanation:

First, let's transform the triangle into a rectangle:

4 4

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=17\times 9$

A=153

$153\div 2= 76.5\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

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Example Question #746 : Geometry

What is the area of the right triangle in the following figure?

Possible Answers:

$114\textup{ in}^2$

$117.5\textup{ in}^2$

$117\textup{ in}^2$

$114.5\textup{ in}^2$

$119\textup{ in}^2$

Correct answer:

$117\textup{ in}^2$

Explanation:

First, let's transform the triangle into a rectangle:

1 1

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=18\times 13$

A=234

$234\div 2= 117\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

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Example Question #747 : Geometry

What is the area of the right triangle in the following figure?

Possible Answers:

$104\textup{ in}^2$

$108\textup{ in}^2$

$102.5\textup{ in}^2$

$106\textup{ in}^2$

$105.5\textup{ in}^2$

Correct answer:

$108\textup{ in}^2$

Explanation:

First, let's transform the triangle into a rectangle:

2 2

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=18\times 12$

A=216

$216\div 2= 108\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

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Example Question #748 : Geometry

What is the area of the right triangle in the following figure?

Possible Answers:

$99\textup{ in}^2$

$105\textup{ in}^2$

$104.5\textup{ in}^2$

$98.5\textup{ in}^2$

$103\textup{ in}^2$

Correct answer:

$99\textup{ in}^2$

Explanation:

First, let's transform the triangle into a rectangle:

3 3

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=18\times 11$

A=198

$198\div 2= 99\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

Report an Error

Example Question #749 : Geometry

What is the area of the right triangle in the following figure?

Possible Answers:

$86.5\textup{ in}^2$

$90\textup{ in}^2$

$88\textup{ in}^2$

$85.5\textup{ in}^2$

$84.5\textup{ in}^2$

Correct answer:

$90\textup{ in}^2$

Explanation:

First, let's transform the triangle into a rectangle:

4 4

Second, let's remember that the formula for area of a rectangle is as follows:

$A=l\times w$

Substitute in our side lengths.

$A=18\times 10$

A=180

$180\div 2= 90\textup{ in}^2$

Thus, the area formula for a right triangle is as follows:

$A=\frac{1}{2}(l\times w)$ or $A=\frac{l\times w}{2}$

Report an Error

Example Question #741 : Geometry

On a number line, what is the length of a line that stretches from $\dpi{100} -3$ to $\dpi{100} 13$ ?

Possible Answers:

$\dpi{100} 3$

$\dpi{100} 16$

$\dpi{100} 13$

$\dpi{100} 10$

Correct answer:

$\dpi{100} 16$

Explanation:

$\dpi{100} -3$ is $\dpi{100} 3$ units to the left of zero on the number line. $\dpi{100} 13$ is $\dpi{100} 13$ units to the right of zero on the number line.

The length of the line would then be $\dpi{100} 13+ 3=16$ .

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All ISEE Lower Level Quantitative Resources

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ISEE Lower Level Quantitative : Geometry

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

All ISEE Lower Level Quantitative Resources

Example Questions

Example Question #741 : Geometry

Example Question #742 : Geometry

Example Question #743 : Geometry

Example Question #744 : Geometry

Example Question #745 : Geometry

Example Question #746 : Geometry

Example Question #747 : Geometry

Example Question #748 : Geometry

Example Question #749 : Geometry

Example Question #741 : Geometry

All ISEE Lower Level Quantitative Resources

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