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. 54 m, 12 m, 21 m, 24 m, 12 m, 9 m, 9 m

Explanation:

Step1: Calculate area of outer rectangle

The outer rectangle has dimensions $54\ \text{m}$ and $24\ \text{m}$.
$\text{Area}_{\text{outer}} = 54 \times 24 = 1296\ \text{m}^2$

Step2: Find base of cut-out trapezoid

First, calculate the missing length for the trapezoid's base:
$54 - 9 - 21 - 12 = 12\ \text{m}$

Step3: Calculate area of cut-out trapezoid

The trapezoid has two parallel sides $12\ \text{m}$ and $21\ \text{m}$, height $9\ \text{m}$.
$\text{Area}_{\text{trapezoid}} = \frac{1}{2} \times (12 + 21) \times 9 = \frac{1}{2} \times 33 \times 9 = 148.5\ \text{m}^2$

Step4: Subtract trapezoid area from outer rectangle

Subtract the cut-out area from the total outer area to get the figure's area.
$\text{Area}_{\text{final}} = 1296 - 148.5 = 1147.5\ \text{m}^2$

Answer:

$1147.5\ \text{m}^2$