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ISEE Lower Level Quantitative : Plane Geometry

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Example Questions

Example Question #511 : Plane Geometry

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

Possible Answers:

$93.5\textup{ in}^2$

$91.5\textup{ in}^2$

$96\textup{ in}^2$

$95\textup{ in}^2$

$90.5\textup{ in}^2$

Correct answer:

$93.5\textup{ in}^2$

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:

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

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 .

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

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 #512 : Plane Geometry

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

Possible Answers:

$83.5\textup{ in}^2$

$89\textup{ in}^2$

$85\textup{ in}^2$

$87.5\textup{ in}^2$

$81\textup{ in}^2$

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 #513 : Plane Geometry

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

Possible Answers:

$78.5\textup{ in}^2$

$74\textup{ in}^2$

$76.5\textup{ in}^2$

$72.5\textup{ in}^2$

$80\textup{ in}^2$

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 #514 : Plane Geometry

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

Possible Answers:

$114.5\textup{ in}^2$

$117\textup{ in}^2$

$117.5\textup{ in}^2$

$119\textup{ in}^2$

$114\textup{ in}^2$

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 #515 : Plane Geometry

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

Possible Answers:

$108\textup{ in}^2$

$102.5\textup{ in}^2$

$105.5\textup{ in}^2$

$106\textup{ in}^2$

$104\textup{ in}^2$

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 #516 : Plane Geometry

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

Possible Answers:

$104.5\textup{ in}^2$

$98.5\textup{ in}^2$

$99\textup{ in}^2$

$103\textup{ in}^2$

$105\textup{ in}^2$

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 $A=\frac{l\times w}{2}$

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Example Question #517 : Plane Geometry

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

Possible Answers:

$84.5\textup{ in}^2$

$86.5\textup{ in}^2$

$90\textup{ in}^2$

$85.5\textup{ in}^2$

$88\textup{ in}^2$

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 $A=\frac{l\times w}{2}$

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Example Question #1 : Lines

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

Possible Answers:

$\dpi{100} 3$

$\dpi{100} 10$

$\dpi{100} 16$

$\dpi{100} 13$

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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Example Question #2 : Lines

If the radius of a circle is equal to $\frac{1}{4}x$ , then what is the value of the diameter?

Possible Answers:

$\frac{1}{2}x$

$\frac{1}{4}x$

Correct answer:

$\frac{1}{2}x$

Explanation:

The length of a dimater is twice the length of the radius. Given that the length of the radius is $\frac{1}{4}x$ , the dimater will be equal to $\frac{1}{4}x\cdot2=\frac{2}{4}x=\frac{1}{2}x$ .

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Example Question #3 : Lines

The length of is and the length of is .

Screenshot_2015-03-29_at_2.20.22_pm

What is the length of in terms of and ?

Possible Answers:

x^2

x+y

y+x

y-x

x-y

Correct answer:

x-y

Explanation:

Using the segment addition postulate, we know that AC+CD=AD . We can substitute and for and and solve for .

Substitute: y+CD=x

Subtract y from both sides:

Simplify: CD=x-y

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ISEE Lower Level Quantitative : Plane Geometry

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

All ISEE Lower Level Quantitative Resources

Example Questions

Example Question #511 : Plane Geometry

Example Question #512 : Plane Geometry

Example Question #513 : Plane Geometry

Example Question #514 : Plane Geometry

Example Question #515 : Plane Geometry

Example Question #516 : Plane Geometry

Example Question #517 : Plane Geometry

Example Question #1 : Lines

Example Question #2 : Lines

Example Question #3 : Lines

All ISEE Lower Level Quantitative Resources

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