Question

what is the surface area of this triangular pyramid? 10 mm 9 mm 10 mm 10 mm 8.7 mm square millimeters submit

Explanation:

Step1: Analyze the base triangle

The base is an equilateral triangle with side length \( 10 \) mm. The height of the base triangle (from the diagram) is \( 8.7 \) mm. The area of a triangle is \( \frac{1}{2} \times \text{base} \times \text{height} \). So, area of base: \( \frac{1}{2} \times 10 \times 8.7 = 43.5 \) square mm.

Step2: Analyze the lateral faces

There are three congruent triangular lateral faces. Each has a base of \( 10 \) mm and a height (slant height) of \( 9 \) mm. The area of one lateral face is \( \frac{1}{2} \times 10 \times 9 = 45 \) square mm. For three faces: \( 3 \times 45 = 135 \) square mm.

Step3: Calculate total surface area

Total surface area is the sum of the base area and the lateral surface area. So, \( 43.5 + 135 = 178.5 \).

Answer:

\( 178.5 \)