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ISEE Middle Level Math : Trapezoids

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Example Questions

Example Question #1 : How To Find The Area Of A Trapezoid

Trapezoid

What is the area of the above trapezoid?

Possible Answers:

$96.48\textrm{ m}^{2}$

$218.36\textrm{ m}^{2}$

$109.18\textrm{ m}^{2}$

$142.04\textrm{ m}^{2}$

$76.32\textrm{ m}^{2}$

Correct answer:

$109.18\textrm{ m}^{2}$

Explanation:

To find the area of a trapezoid, multiply one half (or 0.5, since we are working with decimals) by the sum of the lengths of its bases (the parallel sides) by its height (the perpendicular distance between the bases). This quantity is

$A = 0.5 \cdot (7.2 + 13.4) \cdot 10.6 =0.5 \cdot 20.6 \cdot 10.6 = 109.18\textrm{ m}^{2}$

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Example Question #1 : How To Find The Area Of A Trapezoid

Find the area of the trapezoid:

Question_7

Possible Answers:

Correct answer:

Explanation:

The area of a trapezoid can be determined using the equation $A=\frac{1}{2}(b_1+b_2)h$ .

$A=\frac{1}{2}(6+8)(4)$

$A=\frac{1}{2}(14)(4)$

A=(7)(4)=28

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Example Question #1 : How To Find The Area Of A Trapezoid

Trapezoid

What is the area of the trapezoid?

Possible Answers:

$105\textrm{ m}^{2}$

$198\textrm{ m}^{2}$

$135\textrm{ m}^{2}$

$99\textrm{ m}^{2}$

$63\textrm{ m}^{2}$

Correct answer:

$99\textrm{ m}^{2}$

Explanation:

To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.

$A = \frac{1}{2} \cdot (7 + 15) \cdot 9 = \frac{1}{2} \cdot 22 \cdot 9 = 99 \textrm{ m}^2$

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Example Question #2 : How To Find The Area Of A Trapezoid

Trapezoid

The above diagram depicts a rectangle RECT with isosceles triangle $\Delta ECM$ . If is the midpoint of $\overline{CT}$ , and the area of the orange region is , then what is the length of one leg of $\Delta ECM$ ?

Possible Answers:

$\sqrt {48}$

$\sqrt {54}$

$\sqrt {108}$

$\sqrt {96}$

Correct answer:

$\sqrt {48}$

Explanation:

The length of a leg of $\Delta ECM$ is equal to the height of the orange region, which is a trapezoid. Call this length/height .

Since the triangle is isosceles, then CM = h , and since is the midpoint of $\overline{CT}$ , MT = h . Also, since opposite sides of a rectangle are congruent,

RE = CT = CM + MT = h + h = 2h

Therefore, the orange region is a trapezoid with bases and and height . Its area is 72, so we can set up and solve this equation using the area formula for a trapezoid:

$\frac{1}{2} (B + b)h = 72$

$\frac{1}{2} (2h + h)h = 72$

$\frac{1}{2} (3h )h = 72$

$\frac{3}{2}h^{2} = 72$

$\frac{3}{2}h^{2} \cdot \frac{2}{3} = 72 \cdot \frac{2}{3}$

$h^{2}= 48$

$h = \sqrt {48}$

This is the length of one leg of the triangle.

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Example Question #171 : Plane Geometry

A trapezoid has a height of inches and bases measuring inches and inches. What is its area?

Possible Answers:

$600\; \textrm{in}^{2}$

$1,500\; \textrm{in}^{2}$

$900\; \textrm{in}^{2}$

$750\; \textrm{in}^{2}$

$864\; \textrm{in}^{2}$

Correct answer:

$750\; \textrm{in}^{2}$

Explanation:

Use the following formula, with B = 36,b = 24,h=25 :

$A = \frac{1}{2} (B+b)h = \frac{1}{2} (36+24) \cdot 25 = 750$

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Example Question #3 : How To Find The Area Of A Trapezoid

Find the area of a trapezoid with bases equal to 7 and 9 and height is 2.

Possible Answers:

126

Correct answer:

Explanation:

To solve, simply use the formula for the area of a trapezoid.

b1=7, b2=9, h=2

Thus,

$A=\frac{1}{2}(b1+b2)h=\frac{1}{2}(7+9)(2)=16$

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Example Question #4 : How To Find The Area Of A Trapezoid

Find the area of a trapezoid with bases of 10 centimeters and 8 centimeters, and a height of 4 centimeters.

Possible Answers:

$112cm^{2}$

$36cm^{2}$

$56cm^{2}$

$72cm^{2}$

Correct answer:

$36cm^{2}$

Explanation:

The formula for area of a trapezoid is:

$A=\frac{1}{2} (b_{1}+b_{2}) \times h$

where

b_1=10, b_2=8, h=4

therefore the area equation becomes,

$A = \frac{1}{2} (10 + 8) \times 4$

$A = \frac{1}{2} (72)$

$A = 36cm^{2}$

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Example Question #3 : How To Find The Area Of A Trapezoid

You recently bought a new bookshelf with a base in the shape of an isosceles trapezoid. If the small base is 2 feet, the large base is 3 feet, and the depth is 8 inches, what is the area of the base of your new bookshelf?

Possible Answers:

Cannot be determined from the information provided.

$\frac{5}{2}ft^2$

$\frac{3}{5}ft^2$

$\frac{5}{3}ft^2$

Correct answer:

$\frac{5}{3}ft^2$

Explanation:

To find the area of a trapezoid, we need to use the following formula:

$A_{trapezoid}=\frac{a+b}{2}*h$

Where a and b are the lengths of the bases, and h is the perpendicular distance from one base to another.

We are given a and b, and then h will be the same as our depth. The tricky part is realizing that our depth is in inches, while our base lengths are in feet. We need to convert 8 inches to feet:

$8in*\frac{1ft}{12in}=\frac{8}{12}=\frac{2}{3}ft$

Next, plug it all into our equation up above.

$A_{trapezoid}=\frac{2+3}{2}*\frac{2}{3}=\frac{5}{2}*\frac{2}{3}$

$\frac{5}{2}*\frac{2}{3}=\frac{5}{3}ft^2$

So our answer is:

$\frac{5}{3}ft^2$

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Example Question #1 : How To Find The Area Of A Trapezoid

Rectangles 3

The above diagram shows Rectangle RECT , with midpoint of $\overline{CT}$ .

The area of Quadrilateral REMT is 1,200 . Evaluate .

Possible Answers:

Correct answer:

Explanation:

The easiest way to see this problem is to note that Quadrilateral REMT has as its area that of Rectangle RECT minus that of $\bigtriangleup ECM$ .

The area of Rectangle RECT is its length multiplied by its width:

$2x \cdot \frac{1}{2} x = 2 \cdot \frac{1}{2} \cdot x \cdot x = x^{2}$

is the midpoint of $\overline{CT}$ , so $\bigtriangleup ECM$ has as its base and height $\frac{1}{2} \cdot 2x =x$ and $\frac{1}{2} x$ , respectively;

its area is half their product, or

$\frac{1}{2} \cdot x \cdot \frac{1}{2} x = \frac{1}{4} x^{2}$

The area of Quadrilateral REMT is

$x^{2} - \frac{1}{4} x^{2} = \frac{3}{4} x^{2} = 1,200$ , so

$\frac{3}{4} x^{2} \cdot \frac{4} {3} = 1,200\cdot \frac{4} {3}$

$x^{2} = 1,600$

$x =\sqrt{ 1,600} = 40$

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

The perimeter of the following trapezoid is equal to 23 cm. Solve for . (Figure not drawn to scale.)

Possible Answers:

x=4

x=2

x=8

x=12

Correct answer:

x=4

Explanation:

The perimeter is equal to the sum of all of the sides.

$P=23\: cm$

$P=23\: cm=5+6+x+2x$

23=11+3x

23-11=11+3x-11

12=3x

$\frac{12}{3}=\frac{3x}{3}$

x=4

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ISEE Middle Level Math : Trapezoids

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #1 : How To Find The Area Of A Trapezoid

Example Question #1 : How To Find The Area Of A Trapezoid

Example Question #1 : How To Find The Area Of A Trapezoid

Example Question #2 : How To Find The Area Of A Trapezoid

Example Question #171 : Plane Geometry

Example Question #3 : How To Find The Area Of A Trapezoid

Example Question #4 : How To Find The Area Of A Trapezoid

Example Question #3 : How To Find The Area Of A Trapezoid

Example Question #1 : How To Find The Area Of A Trapezoid

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

All ISEE Middle Level Math Resources

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