Question

formula for the area of a parallelogram: $a = bh$
example:
the height is measured straight up from the base. the height of this parallelogram is 4 m.
$a = bh$
$a = 8\bullet4$
$a = 32\\ \text{m}^2$
find the perimeter and the area of each parallelogram. for the area, show all steps.
1.
2.
3.
4.
5.
6.

1. the base of a parallelogram is 10 in. the height is 2 in. more than half the base. find the area.
2. the height of a parallelogram is 4.5 cm. the base is twice the height. what is the area?
3. the area of a parallelogram is $60\\ \text{ft}^2$. the height is 5 ft. how long is the base?
4. the area of a parallelogram is $275\\ \text{cm}^2$. the base is 25 cm. find the height.

Explanation:

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Problem 1

Step1: Calculate area (base=16 ft, height=8 ft)

$A = bh = 16 \times 8 = 128$ ft²

Step2: Calculate perimeter (sides=16 ft,10 ft)

$P = 2(16 + 10) = 2 \times 26 = 48$ ft

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Problem 2

Step1: Calculate area (base=12 m, height=15 m)

$A = bh = 12 \times 15 = 180$ m²

Step2: Calculate perimeter (sides=12 m,16 m)

$P = 2(12 + 16) = 2 \times 28 = 56$ m

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Problem 3

Step1: Calculate area (base=5.1 cm, height=3.2 cm)

$A = bh = 5.1 \times 3.2 = 16.32$ cm²

Step2: Calculate perimeter (sides=5.1 cm,3.6 cm)

$P = 2(5.1 + 3.6) = 2 \times 8.7 = 17.4$ cm

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Problem 4

Step1: Calculate area (base=9.3 cm, height=6.5 cm)

$A = bh = 9.3 \times 6.5 = 60.45$ cm²

Step2: Calculate perimeter (sides=9.3 cm,7.5 cm)

$P = 2(9.3 + 7.5) = 2 \times 16.8 = 33.6$ cm

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Problem 5

Step1: Calculate area (base=100 ft, height=90 ft)

$A = bh = 100 \times 90 = 9000$ ft²

Step2: Calculate perimeter (sides=100 ft,90 ft)

$P = 2(100 + 90) = 2 \times 190 = 380$ ft

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Problem 6

Step1: Calculate area (base=0.7 m, height=1.8 m)

$A = bh = 0.7 \times 1.8 = 1.26$ m²

Step2: Calculate perimeter (sides=0.7 m,2.0 m)

$P = 2(0.7 + 2.0) = 2 \times 2.7 = 5.4$ m

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Problem 7

Step1: Calculate height (half base +2 in)

$h = \frac{10}{2} + 2 = 5 + 2 = 7$ in

Step2: Calculate area (base=10 in, height=7 in)

$A = bh = 10 \times 7 = 70$ in²

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Problem 8

Step1: Calculate base (twice height)

$b = 2 \times 4.5 = 9$ cm

Step2: Calculate area (base=9 cm, height=4.5 cm)

$A = bh = 9 \times 4.5 = 40.5$ cm²

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Problem 9

Step1: Rearrange area formula for base

$b = \frac{A}{h}$

Step2: Calculate base (A=60 ft², h=5 ft)

$b = \frac{60}{5} = 12$ ft

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Problem 10

Step1: Rearrange area formula for height

$h = \frac{A}{b}$

Step2: Calculate height (A=275 cm², b=25 cm)

$h = \frac{275}{25} = 11$ cm

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Answer:

1. Area = 128 ft², Perimeter = 48 ft
2. Area = 180 m², Perimeter = 56 m
3. Area = 16.32 cm², Perimeter = 17.4 cm
4. Area = 60.45 cm², Perimeter = 33.6 cm
5. Area = 9000 ft², Perimeter = 380 ft
6. Area = 1.26 m², Perimeter = 5.4 m
7. Area = 70 in²
8. Area = 40.5 cm²
9. Base = 12 ft
10. Height = 11 cm