Question

A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 9 yards long, and the height of the equilateral triangle is 7.8 yards. The pyramid's slant height is 14 yards. What is its surface area?

a) ( 243 , sq. yards )
b) ( 256 , sq. yards )
c) ( 274 , sq. yards )
d) ( 289 , sq. yards )

Answer 1

The surface area of a triangular pyramid with an equilateral triangle base of 9 yards, a base height of 7.8 yards, and a slant height of 14 yards is 224 square yards. None of the provided multiple-choice options are correct.

Step-by-step explanation:

To calculate the surface area of a triangular pyramid with an equilateral triangle base, we use the formula for the area of a triangle, which is 1/2 × base × height, and then add the area of the three triangular faces that make up the sides of the pyramid. The base's area can be calculated as 1/2 × 9 yards × 7.8 yards. Each side face can be calculated using the slant height as the height of the triangle and one side of the base as the base of the triangle. Therefore, the area for one side face is 1/2 × 9 yards × 14 yards. The total surface area of the pyramid is the area of the base plus the area of the three side faces.

The area of the base is: 1/2 × 9 × 7.8 = 35.1 square yards.

To find the area of one triangular side face: 1/2 × 9 × 14 = 63 square yards.

Since there are three side faces: 63 × 3 = 189 square yards for all side faces.

Adding the base area to the side faces area gives us the total surface area: 35.1 + 189 = 224.1 square yards rounded down would be 224 square yards, making none of the provided options correct.