Question

what is the area of the figure below? figure with dimensions: top square (3 in. × 3 in.), middle section with height 5 in., bottom square (3 in. × 3 in.), and total width at bottom 7 in.; options: 68 in.², 88 in.², 48 in.², 43 in.²

Explanation:

Step1: Area of top square

The top figure is a square with side 3 in. Area of square is $side^2$. So area is $3\times3 = 9$ in².

Step2: Area of bottom square

The bottom figure is also a square with side 3 in. Area is $3\times3 = 9$ in².

Step3: Area of middle trapezoid (upper)

The upper trapezoid has bases 3 in and 7 in, height 5 in. Area of trapezoid is $\frac{(a + b)}{2}\times h$. So $\frac{(3 + 7)}{2}\times5=\frac{10}{2}\times5 = 25$ in².

Step4: Area of middle trapezoid (lower)

The lower trapezoid is same as upper, bases 3 in and 7 in, height 5 in. Area is also $\frac{(3 + 7)}{2}\times5 = 25$ in².

Step5: Total area

Sum all areas: $9 + 9 + 25 + 25 = 68$ in².

Answer:

68 in²