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)
