Question

trapezoid - area
find the area of each trapezoid.
1)
4 in

15 in 8 in
area =
2)
12 ft

18 ft 7 ft
area =
3)
20 yd

10 yd 14 yd
area =
4)
11 ft

16 ft 19 ft
area =
5)
5 yd

17 yd 13 yd
area =
6)
9 in

2 in 6 in
area =

1. the height of a trapezoid is 12 yards. find the area of the trapezoid if the lengths of the parallel bases are 3 yards and 17 yards.

1. the sum of the bases of a trapezoid is 17 feet. determine the area of the trapezoid if the perpendicular distance between the bases is 15 feet.

Explanation:

The formula for the area of a trapezoid is $A = \frac{1}{2}(b_1 + b_2)h$, where $b_1$ and $b_2$ are the lengths of the parallel bases, and $h$ is the perpendicular height between them.

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1)

Step1: Identify values

$b_1=4$ in, $b_2=15$ in, $h=8$ in

Step2: Substitute into formula

$A = \frac{1}{2}(4 + 15) \times 8$

Step3: Calculate

$A = \frac{1}{2} \times 19 \times 8 = 76$

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2)

Step1: Identify values

$b_1=12$ ft, $b_2=18$ ft, $h=7$ ft

Step2: Substitute into formula

$A = \frac{1}{2}(12 + 18) \times 7$

Step3: Calculate

$A = \frac{1}{2} \times 30 \times 7 = 105$

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3)

Step1: Identify values

$b_1=20$ yd, $b_2=10$ yd, $h=14$ yd

Step2: Substitute into formula

$A = \frac{1}{2}(20 + 10) \times 14$

Step3: Calculate

$A = \frac{1}{2} \times 30 \times 14 = 210$

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4)

Step1: Identify values

$b_1=11$ ft, $b_2=19$ ft, $h=16$ ft

Step2: Substitute into formula

$A = \frac{1}{2}(11 + 19) \times 16$

Step3: Calculate

$A = \frac{1}{2} \times 30 \times 16 = 240$

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5)

Step1: Identify values

$b_1=5$ yd, $b_2=17$ yd, $h=13$ yd

Step2: Substitute into formula

$A = \frac{1}{2}(5 + 17) \times 13$

Step3: Calculate

$A = \frac{1}{2} \times 22 \times 13 = 143$

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6)

Step1: Identify values

$b_1=6$ in, $b_2=9$ in, $h=2$ in

Step2: Substitute into formula

$A = \frac{1}{2}(6 + 9) \times 2$

Step3: Calculate

$A = \frac{1}{2} \times 15 \times 2 = 15$

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7)

Step1: Identify values

$b_1=3$ yd, $b_2=17$ yd, $h=12$ yd

Step2: Substitute into formula

$A = \frac{1}{2}(3 + 17) \times 12$

Step3: Calculate

$A = \frac{1}{2} \times 20 \times 12 = 120$

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8)

Step1: Identify values

$b_1 + b_2=17$ ft, $h=15$ ft

Step2: Substitute into formula

$A = \frac{1}{2} \times 17 \times 15$

Step3: Calculate

$A = 127.5$

Answer:

1. $76$ square inches
2. $105$ square feet
3. $210$ square yards
4. $240$ square feet
5. $143$ square yards
6. $15$ square inches
7. $120$ square yards
8. $127.5$ square feet