For a project, gabrielle made a model of an egyptian pyramid. the square base has a side length measuring 10 inches. the pyramid is 12 inches tall. what is the surface area of the model? 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

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.

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