Question

1. calculate the area of the trapezoid:top base 4 mm, bottom base 7 mm, height 2 mm.$a =$2. calculate the area of the trapezoid:top base 9 m, bottom base 5 m, height 6 m.$a =$3. calculate the area of the trapezoid:top base 1 km, bottom base 2 km, height 8 km.$a =$4. calculate the area of the trapezoid:top base 8 cm, bottom base 6 cm, height 5 cm.$a =$

Explanation:

Step1: Recall trapezoid area formula

The area of a trapezoid is given by $A = \frac{1}{2} \times (b_1 + b_2) \times h$, where $b_1$ and $b_2$ are the lengths of the two parallel sides, and $h$ is the height (perpendicular distance between the parallel sides).

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Step1 (First trapezoid): Plug in values

$b_1=4\ \text{mm}$, $b_2=7\ \text{mm}$, $h=2\ \text{mm}$
$A = \frac{1}{2} \times (4 + 7) \times 2$

Step2: Simplify calculation

$A = \frac{1}{2} \times 11 \times 2 = 11\ \text{mm}^2$

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Step1 (Second trapezoid): Plug in values

$b_1=9\ \text{m}$, $b_2=5\ \text{m}$, $h=6\ \text{m}$
$A = \frac{1}{2} \times (9 + 5) \times 6$

Step2: Simplify calculation

$A = \frac{1}{2} \times 14 \times 6 = 42\ \text{m}^2$

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Step1 (Third trapezoid): Plug in values

$b_1=1\ \text{km}$, $b_2=2\ \text{km}$, $h=8\ \text{km}$
$A = \frac{1}{2} \times (1 + 2) \times 8$

Step2: Simplify calculation

$A = \frac{1}{2} \times 3 \times 8 = 12\ \text{km}^2$

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Step1 (Fourth trapezoid): Plug in values

$b_1=8\ \text{cm}$, $b_2=6\ \text{cm}$, $h=5\ \text{cm}$
$A = \frac{1}{2} \times (8 + 6) \times 5$

Step2: Simplify calculation

$A = \frac{1}{2} \times 14 \times 5 = 35\ \text{cm}^2$

Answer:

1. $11\ \text{mm}^2$
2. $42\ \text{m}^2$
3. $12\ \text{km}^2$
4. $35\ \text{cm}^2$