Question

practice
find the area of each parallelogram. (example 1)
1.
2.

1. the parallelogram - shaped learning toy belonging to marcos baby brother has the dimensions shown. what is the base length of the toy? (example 2)
2. the dimensions of a parallelogram - shaped tabletop are shown. what is the distance across the tabletop? (example 3)

find the area of each trapezoid. (example 3)
5.
6.

Explanation:

Step1: Use parallelogram area formula

The area of a parallelogram is $A = b \times h$, where $b$ is the base and $h$ is the corresponding height.

Step1 (Problem 1): Substitute given values

Base $b=8$ m, height $h=10$ m.
$A = 8 \times 10$

Step2 (Problem 1): Calculate the area

$A = 80$
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Step1 (Problem 2): Substitute given values

Base $b=10$ in, height $h=9$ in.
$A = 10 \times 9$

Step2 (Problem 2): Calculate the area

$A = 90$
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Step1 (Problem 3): Rearrange area formula for base

$b = \frac{A}{h}$, where $A=72$ cm², $h=8$ cm.
$b = \frac{72}{8}$

Step2 (Problem 3): Calculate the base length

$b = 9$
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Step1 (Problem 4): Rearrange area formula for height

$h = \frac{A}{b}$, where $A=720$ in², $b=36$ in.
$h = \frac{720}{36}$

Step2 (Problem 4): Calculate the height

$h = 20$
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Step1 (Problem 5): Find the lower base length

Lower base $= 7 + 5 + 2 = 14$ m.

Step2 (Problem 5): Use trapezoid area formula

Trapezoid area $A = \frac{1}{2}(b_1 + b_2)h$, where $b_1=7$ m, $b_2=14$ m, $h=6$ m.
$A = \frac{1}{2}(7 + 14) \times 6$

Step3 (Problem 5): Simplify and calculate

$A = \frac{1}{2} \times 21 \times 6 = 63$
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Step1 (Problem 6): Find the lower base length

Lower base $= 9 + 3 + 3 = 15$ ft.

Step2 (Problem 6): Use trapezoid area formula

Trapezoid area $A = \frac{1}{2}(b_1 + b_2)h$, where $b_1=9$ ft, $b_2=15$ ft, $h=6$ ft.
$A = \frac{1}{2}(9 + 15) \times 6$

Step3 (Problem 6): Simplify and calculate

$A = \frac{1}{2} \times 24 \times 6 = 72$

Answer:

1. $\boldsymbol{80}$ square meters
2. $\boldsymbol{90}$ square inches
3. $\boldsymbol{9}$ centimeters
4. $\boldsymbol{20}$ inches
5. $\boldsymbol{63}$ square meters
6. $\boldsymbol{72}$ square feet