Answer: 57 cm²
Step-by-step explanation:
To answer this question, we need to find the surface area of the figure.
First, we will find the surface area of the bottom part, the rectangular prism. We will use the given formula. However, we do not count the top side since it is connected to the bottom part. We will subtract this.
SA = 2(wl + hl + hw)
SA = 2((3 cm)(3 cm) + (2 cm)(3 cm) + (2 cm)(3 cm))
SA = 42 cm²
SA = 42 cm² - 9 cm² = 33 cm²
Next, we will find the surface area of the top part, the square pyramid. We know we have four congruent triangles. We will not count the square base since it is connected to the bottom part.
SA = 4 * ([tex]\frac{bh}{2}[/tex])
SA = 2 * (bh)
SA = 2 * ((3 cm)(4 cm))
SA = 2 * (12 cm²)
SA = 24 cm²
Lastly, we will add these two parts together.
33 cm² + 24 cm² = 57 cm²
