Question

what is the surface area of this shap type your answer in the boxes

Explanation:

Step1: Identify the shape (right triangular prism)

The shape is a right triangular prism with a right triangle base (legs 6, 8, hypotenuse 10) and length 12.

Step2: Calculate base area (triangle)

Area of one triangular base: $\frac{1}{2} \times 6 \times 8 = 24$. Two bases: $2 \times 24 = 48$.

Step3: Calculate lateral surface areas

• Area of rectangle with length 12 and width 6: $12 \times 6 = 72$.
• Area of rectangle with length 12 and width 8: $12 \times 8 = 96$.
• Area of rectangle with length 12 and width 10: $12 \times 10 = 120$.

Step4: Sum all areas

Total surface area: $48 + 72 + 96 + 120 = 336$.

Answer:

336