Question

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Answer 1

Answer:

$153\ in^2$

Step-by-step explanation:

1. Approach

Divide the given figure up into two simple figures, a trapezoid, and a rectangle. Calculate the area of each figure by using their respective area formula. Then add up the results to get the value for the area of the entire figure.

2. Area of the trapezoid

The first figure is a trapezoid, calculate its area by using the following formula,

$A_t= \frac{b_1+b_2}{2}(h)$

Where parameters ($b_1$) and ($b_2$) represent the base of the trapezoid, and ($h$) represents the height. Substitute in the given values and solve.

$A_t = \frac{16 + 5}{2}(10)$

Simplify,

$=\frac{21}{2}(10)$

$=10.5(10)$

$=105$

3. Area of the rectangle

The other figure formed by the partition of the two figures is a rectangle. The formula to find the area of a rectangle is the following,

$A_r =(b)(h)$

Where ($b$) represents the base of the figure, and ($h$) represents the height of the figure. Substitute in the values for the given parameters and solve,

$A_r=(16)(3)$

Simplify,

$=48$

4. Find the total area

Now add up the values for the area of each figure. The result will be the total area of the figure,

$A_t + A_r = A$

Substitute,

$105 + 48 = A$

Simplify,

$153 = A$