Question

find the area of the geometric figure.
diagram of a composite geometric figure with labeled sides: 4 cm (top of square), 4 cm (side of square), 9 cm (slant side of parallelogram), 4 cm (base of parallelogram)
the area is
(simplify your answer.)
hw score: 56.9%, 33 of 58 points
question 28, 6.4.23
points: 0 of 1
unit 3 - geometry

Explanation:

Step1: Identify the two shapes (square and parallelogram)

The figure consists of a square (top) and a parallelogram (bottom). For the square: side length \( s = 4 \, \text{cm} \), area of square \( A_{\text{square}} = s^2 \). For the parallelogram: base \( b = 4 \, \text{cm} \), height \( h = 9 \, \text{cm} \), area of parallelogram \( A_{\text{parallelogram}} = b \times h \).

Step2: Calculate area of square

\( A_{\text{square}} = 4^2 = 16 \, \text{cm}^2 \)

Step3: Calculate area of parallelogram

\( A_{\text{parallelogram}} = 4 \times 9 = 36 \, \text{cm}^2 \)

Step4: Sum the areas

Total area \( A = A_{\text{square}} + A_{\text{parallelogram}} = 16 + 36 = 52 \, \text{cm}^2 \)

Answer:

\( 52 \) square centimeters (or \( 52 \, \text{cm}^2 \))