Question

is rain correct? use the drop - down menus to explain your reasoning. there are some geometric figures with side lengths and heights marked, like 10 in, 13 in, 12 in, 8.7 in, and some area - related expressions like 3(\frac{1}{2}×10×13)+(\frac{1}{2}×10×8.7), 3(65)+43.5, 238.5

Explanation:

Step1: Identify correct surface area components

The figure is a triangular pyramid (4 triangular faces: 3 congruent triangles with base 10 in, height 12 in, and 1 triangle with base 10 in, height 8.7 in).

Step2: Calculate area of 3 congruent faces

Area of 1 face: $\frac{1}{2} \times 10 \times 12 = 60$ in²
Total for 3 faces: $3 \times 60 = 180$ in²

Step3: Calculate area of the base face

$\frac{1}{2} \times 10 \times 8.7 = 43.5$ in²

Step4: Sum all face areas

Total surface area: $180 + 43.5 = 223.5$ in²

Step5: Compare with Rain's calculation

Rain incorrectly used 13 in as height for the 3 congruent faces instead of 12 in.

Answer:

Rain is not correct. The correct total surface area is 223.5 square inches, while Rain's calculation used the wrong height (13 in instead of 12 in) for the three congruent triangular faces, leading to an overestimated value of 238.5 square inches.