Question

what is the surface area of this figure?
a) 236 cm²
b) 364 cm²
c) 1800 cm²

d the total surface area of the prism.
a) 186 square feet
b) 161 square feet
c) 75 square feet
d) 1,700 square feet

Explanation:

Step1: Calculate base triangle area

The base is a right triangle, area = $\frac{1}{2} \times 5 \times 5 = 12.5$ square feet.

Step2: Calculate 2 bases total area

Total base area = $2 \times 12.5 = 25$ square feet.

Step3: Calculate lateral face areas

Lateral faces:

1. $5 \times 8 = 40$ square feet
2. $5 \times 8 = 40$ square feet
3. $7 \times 8 = 56$ square feet

Step4: Sum lateral face areas

Total lateral area = $40 + 40 + 56 = 136$ square feet.

Step5: Total surface area

Add base and lateral areas: $25 + 136 = 161$ square feet.

Answer:

b) 161 square feet