Question

what is the area of this figure? provide an answer accurate to the nearest tenth. use 3.14 or a calculator button for pi if needed. 4 in 6 in 14 in 14 in 8 in 8 in 14 in 16 in 8 in 6 in label required

Explanation:

Step1: Calculate area of rectangle

First, find the total length of the rectangle: $14 + 4 + 14 = 32$ in.
Area formula: $A = l \times w$
$A_{rectangle} = 32 \times 8 = 256$ in²

Step2: Calculate area of trapezoid

Trapezoid area formula: $A = \frac{1}{2}(a + b)h$
Here, $a=4$ in, $b=14-6+4=12$ in, $h=6$ in
$A_{trapezoid} = \frac{1}{2}(4 + 12) \times 6 = 48$ in²

Step3: Calculate area of parallelogram

Parallelogram area formula: $A = b \times h$
Here, $b=6$ in, $h=8$ in
$A_{parallelogram} = 6 \times 8 = 48$ in²

Step4: Sum all areas

Total area: $256 + 48 + 54 = 358.0$ in²

Answer:

358.0 square inches