Question

what is the area of this figure?
image of a composite geometric figure with labeled side lengths: 5 ft, 3 ft, 2 ft, 3 ft, 2 ft, 4 ft, 4 ft, 6 ft
write your answer using decimals, if necessary.
blank square feet
submit
work it out

Explanation:

Step1: Split into simpler shapes

Divide the figure into a rectangle, a trapezoid, and another rectangle.

Step2: Calculate area of right rectangle

Area = length × width = $4 \times (4+2+2) = 32$ sq ft

Step3: Calculate area of middle trapezoid

Bases: $4+2=6$ ft, $4$ ft; height = $3$ ft.
Area = $\frac{1}{2} \times (6+4) \times 3 = 15$ sq ft

Step4: Calculate area of left trapezoid

Bases: $5$ ft, $4+2=6$ ft; height = $3$ ft.
Area = $\frac{1}{2} \times (5+6) \times 3 = 16.5$ sq ft

Step5: Sum all areas

Total area = $32 + 15 + 16.5$

Answer:

63.5 square feet