Find the surface area of a triangular pyramid with base 10, a base height of 8.7, and a slant height of 12.(1 point)
Responses
103.5
103.5
232.2
232.2
216.6
216.6
223.5
223.5
To find the surface area of a triangular pyramid, we need to find the area of the triangular base and the areas of the three triangular faces.
The area of the triangular base can be found using the formula for the area of a triangle: (1/2) * base * height. In this case, the base of the triangle is given as 10 and the height is given as 8.7. So, the area of the base is (1/2) * 10 * 8.7 = 43.5.
To find the area of each triangular face, we can use the formula for the area of a triangle: (1/2) * base * height. In this case, the base of each face is given as 10 (since it is the same as the base of the triangular base) and the height is given as the slant height, which is 12. So, the area of each face is (1/2) * 10 * 12 = 60.
Since the pyramid has three faces, the total area of the faces is 3 * 60 = 180.
Finally, to find the surface area of the pyramid, we add the area of the base to the total area of the faces: 43.5 + 180 = 223.5.
So, the correct answer is 223.5.