Answer and Explanation:
1) The perimeter is the sum of the base's side lengths, so it is:
P = 10 ft * 4 = 40 ft
2) The height can be calculated using the Pythagorean Theorem. Take half of the base's side length for the short leg (5 ft) and the slant height (13 ft) for the hyptenuse:
5^2 + h^2 = 13^2
25 + h^2 = 169
h^2 = 144
h = 12 ft
3) To find the lateral area, take the area of one of the triangular faces of the pyramid and multiply it by 4, since there are 4 triangular faces:
LA = 4 * (1/2)(10 * 13)
= 4 * 65
= 260 ft
4) The area of the base is the product of its dimensions:
A(base) = 10 * 10
= 100 ft^2
5) Surface area is the sum of the lateral area and the base's area, so just plug in the values from problems 3 and 4:
SA = LA + A(base)
= 260 + 100
= 360 ft^2
