Question

Find the total surface area of the following pyramids: A regular triangular pyramid has base edges of length 30 and height 10.

Answer 1

Answer:

1130 units²

Step-by-step explanation:

SA = sum of area of 4 triangles.

All sides equal means it's an equlateral triangle, which has all angles 60)

1 in the base:

A1 = ½(30)(30)sin(60) = 225sqrt(3)

3 slant triangles:

base = 30

Height to be obtained using pythagoras theorem:

Perpendcular distance of the edge from the mid of the base = ½(distance of one vertex from the midpoint of the opposite edge)

Let the distance of a vertex form the midpoint of the edge opposite to it 'd'

30² = 15² + d²

d² = 675

d = 15sqrt(3)

d/2 = 15sqrt(3)/2

height² = 10² + [15sqrt(3)/2]²

height² = 268.75

height = sqrt(268.75) = 16.4

Area of 1 slant triangle:

A2 = ½(30)(16.4) = 246

SA = A1 + 3 A2

= 225sqrt(3) + 3(246)

= 1127.7 units²

= 1130 units² (3sf)