Question

what is the area of this figure?
write your answer using decimals, if necessary.
□ square feet

Explanation:

Step1: Split into 3 shapes: rect1, rect2, trapezoid

First, identify the three components:

1. Top small rectangle: width $3$ ft, height $6 - (7-2) = 1$ ft
2. Right large rectangle: width $3+2=5$ ft, height $7-2=5$ ft
3. Bottom trapezoid: bases $4$ ft and $3$ ft, height $6$ ft

Step2: Calculate area of rect1

Area = length $\times$ width
$\text{Area}_1 = 3 \times 1 = 3$ square feet

Step3: Calculate area of rect2

Area = length $\times$ width
$\text{Area}_2 = 5 \times 5 = 25$ square feet

Step4: Calculate area of trapezoid

Area = $\frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height}$
$\text{Area}_3 = \frac{1}{2} \times (4 + 3) \times 6 = 21$ square feet

Step5: Sum all areas

Total area = $\text{Area}_1 + \text{Area}_2 + \text{Area}_3$
$\text{Total Area} = 3 + 25 + 21$

Answer:

49 square feet