Question

find the area of the geometric figure.
image of a composite geometric figure with dimensions: top square (2 cm side), bottom parallelogram (base 2 cm, side 5 cm, right angle at base)
the area is
(simplify your answer.)
question 28, 6.4.23
hw score: 63.79%, 37 of 58 points
points: 0 of 1
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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 \( s = 2 \, \text{cm} \). Area of square: \( A_{\text{square}} = s^2 \). For the parallelogram: base \( b = 2 \, \text{cm} \), height \( h = 5 \, \text{cm} \). Area of parallelogram: \( A_{\text{parallelogram}} = b \times h \).

Step2: Calculate area of square

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

Step3: Calculate area of parallelogram

\( A_{\text{parallelogram}} = 2 \times 5 = 10 \, \text{cm}^2 \)

Step4: Sum the areas

Total area \( A = A_{\text{square}} + A_{\text{parallelogram}} = 4 + 10 = 14 \, \text{cm}^2 \)

Answer:

\( 14 \) square centimeters (or \( 14 \, \text{cm}^2 \))