Question

A net of a squared-based pyramid is shown below.
What is the surface area, in square meters, of the pyramid?
15m is the square and 10m is the pyramid

Answer 1

To find the surface area of a pyramid, we need to calculate the area of each face and then sum them up.

1. Base: The base of the pyramid is a square with side length 15m.
Area of base = side length^2 = 15^2 = 225 square meters

2. Each triangle face: To calculate the area of the triangle face, we first need to find the slant height of the pyramid. This can be found using the Pythagorean theorem.
Slant height = sqrt( (1/2 * side length)^2 + height^2)
= sqrt( (1/2 * 15)^2 + 10^2)
= sqrt( (7.5)^2 + 100)
= sqrt( 56.25 + 100)
= sqrt( 156.25)
= 12.5m

Now, we can find the area of each triangle face using the formula:
Area of triangle face = 1/2 * base * height
= 1/2 * 15 * 12.5
= 93.75 square meters

Now, we can sum up the areas of the base and the four triangle faces to find the total surface area of the pyramid:
Total surface area = Area base + 4 * Area triangle face
= 225 + 4 * 93.75
= 225 + 375
= 600 square meters

Therefore, the surface area of the pyramid is 600 square meters.