Trapezoids

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ISEE Upper Level Quantitative Reasoning › Trapezoids

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Trapezoidr

Find the area of the above trapezoid if $a=12\ cm$ , $b=14\ cm$ , and $h=10\ cm$ .

Figure not drawn to scale.

$130\ cm^2$

$120\ cm^2$

$110\ cm^2$

$100\ cm^2$

$90\ cm^2$

Explanation

The area of a trapezoid is given by

$Area=(\frac{b_{1}+b_{2}}{2})h$ ,

where , are the lengths of each base and is the altitude (height) of the trapezoid.

$b_{1}=a=12\ cm$

$b_{2}=b=14\ cm$

$h=10\ cm$

$Area=(\frac{b_{1}+b_{2}}{2})h=(\frac{12+14}{2})\times 10=13\times 10=130\ cm^2$

Trapezoidr

Find the area of the above trapezoid if $a=12\ cm$ , $b=14\ cm$ , and $h=10\ cm$ .

Figure not drawn to scale.

$130\ cm^2$

$120\ cm^2$

$110\ cm^2$

$100\ cm^2$

$90\ cm^2$

Explanation

The area of a trapezoid is given by

$Area=(\frac{b_{1}+b_{2}}{2})h$ ,

where , are the lengths of each base and is the altitude (height) of the trapezoid.

$b_{1}=a=12\ cm$

$b_{2}=b=14\ cm$

$h=10\ cm$

$Area=(\frac{b_{1}+b_{2}}{2})h=(\frac{12+14}{2})\times 10=13\times 10=130\ cm^2$

A trapezoid has the base lengths of and . The area of the trapezoid is . Give the height of the trapezoid in terms of .

Explanation

The area of a trapezoid is given by

$Area=(\frac{b_{1}+b_{2}}{2})h$ ,

where $b_{}1$ , $b_{}2$ are the lengths of each base and is the altitude (height) of the trapezoid.

$Area=(\frac{b_{1}+b_{2}}{2})h=(\frac{3t+t}{2})\times h=8t^2\Rightarrow (2t)h=8t^2$

$\Rightarrow h=\frac{8t^2}{2t}=4t$

A trapezoid has the base lengths of and . The area of the trapezoid is . Give the height of the trapezoid in terms of .

Explanation

The area of a trapezoid is given by

$Area=(\frac{b_{1}+b_{2}}{2})h$ ,

where $b_{}1$ , $b_{}2$ are the lengths of each base and is the altitude (height) of the trapezoid.

$Area=(\frac{b_{1}+b_{2}}{2})h=(\frac{3t+t}{2})\times h=8t^2\Rightarrow (2t)h=8t^2$

$\Rightarrow h=\frac{8t^2}{2t}=4t$

In the following trapezoid and . The area of the trapezoid is 54 square inches. Give the height of the trapezoid. Figure not drawn to scale.

Trap

$6\ in$

$5\ in$

$4\ in$

$7\ in$

$3\ in$

Explanation

The area of a trapezoid is given by

$Area=(\frac{b_{1}+b_{2}}{2})h$ ,

where $b_{}1$ , $b_{}2$ are the lengths of each base and is the altitude (height) of the trapezoid.

$b_{1}=a$

$b_{2}=b=2a$

Substitute these values into the area formula:

$Area=(\frac{b_{1}+b_{2}}{2})h=(\frac{a+2a}{2})a=54\Rightarrow \frac{3a^2}{2}=54\Rightarrow a^2=36\Rightarrow a=6\ in$

In the following trapezoid and . The area of the trapezoid is 54 square inches. Give the height of the trapezoid. Figure not drawn to scale.

Trap

$6\ in$

$5\ in$

$4\ in$

$7\ in$

$3\ in$

Explanation

The area of a trapezoid is given by

$Area=(\frac{b_{1}+b_{2}}{2})h$ ,

where $b_{}1$ , $b_{}2$ are the lengths of each base and is the altitude (height) of the trapezoid.

$b_{1}=a$

$b_{2}=b=2a$

Substitute these values into the area formula:

$Area=(\frac{b_{1}+b_{2}}{2})h=(\frac{a+2a}{2})a=54\Rightarrow \frac{3a^2}{2}=54\Rightarrow a^2=36\Rightarrow a=6\ in$

Trapezoid

Note: Figure NOT drawn to scale.

The above trapezoid has area . What is ?

Explanation

Substitute in the formula for the area of a trapezoid:

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

$\frac{1}{2} (16 + 12)h = 98$

$\frac{1}{2} (28)h = 98$

$14h \div 14= 98 \div 14$

Trapezoid

Note: Figure NOT drawn to scale.

The area of the above trapezoid is . What is ?

Explanation

Substitute into the formula for the area of a trapezoid:

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

$\frac{1}{2} (B + 25) \cdot 15 = 465$

$2 \cdot \frac{1}{2} (B + 25) \cdot 15 = 2 \cdot 465$

$(B + 25) \cdot 15 = 930$

$15 B \div 15 = 555\div 15$

Trapezoid

Note: Figure NOT drawn to scale.

The area of the above trapezoid is . What is ?

Explanation

Substitute into the formula for the area of a trapezoid:

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

$\frac{1}{2} (B + 25) \cdot 15 = 465$

$2 \cdot \frac{1}{2} (B + 25) \cdot 15 = 2 \cdot 465$

$(B + 25) \cdot 15 = 930$

$15 B \div 15 = 555\div 15$

Trapezoid

Note: Figure NOT drawn to scale.

The above trapezoid has area . What is ?

Explanation

Substitute in the formula for the area of a trapezoid:

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

$\frac{1}{2} (16 + 12)h = 98$

$\frac{1}{2} (28)h = 98$

$14h \div 14= 98 \div 14$

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