Question

marie made a model (shown below) of the square pyramid she plans to build when she grows up. find the surface area of the model. 12 m 8 m 12 m m²

Explanation:

Step1: Calculate base area

The base is a square with side - length $s = 12$ m. The area of the base $A_{base}=s^{2}=12^{2}=144$ m².

Step2: Calculate area of one triangular face

The formula for the area of a triangle is $A=\frac{1}{2}bh$. Here, the base of each triangular face $b = 12$ m and the height $h = 8$ m. So the area of one triangular face $A_{triangle}=\frac{1}{2}\times12\times8 = 48$ m².

Step3: Calculate total area of triangular faces

A square - pyramid has 4 triangular faces. The total area of the 4 triangular faces $A_{triangles}=4\times A_{triangle}=4\times48 = 192$ m².

Step4: Calculate surface area

The surface area $A$ of the square - pyramid is the sum of the base area and the total area of the triangular faces. So $A = A_{base}+A_{triangles}=144 + 192=336$ m².

Answer:

336