The surface area of a pyramid may be calculated using the formula: Area = length * width + length*√[(width/2)² + height²] + width*√[(length/2)² + height²]
In this case, the base of the pyramid is a square, which means that the length and the width are equivalent. Therefore, the equation simplifies: Area = l² + 2l√[(l/2)² + h²]
Now, we substitute the values into the equation: A = 10² + 2*10*√[(10/2)² + 12²] A = 360
The surface area of the pyramid is 360 square inches.
The pyramid is shown in the diagram below. The pyramid is built from four congruent triangles and one square as the base
We have the side of the square, so the area is = 10×10 = 100
We need the height of the triangle to work out its area. We can find out by using the height of the pyramid and half of the length of the side of the square.
Using the Pythagoras rule Height of triangle =
Area of one triangle = 1/2×10×12=60 Surface area of the pyramid = 100 + (4×60) = 340 square inches