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. m² 8 m 5 m 8 m

Explanation:

Step1: Calculate base area

The base is a square with side - length $s = 8$ m. The area of the base $A_{base}=s^2$. So, $A_{base}=8^2 = 64$ m².

Step2: Calculate area of one triangular face

The triangular faces have base $b = 8$ m and height $h = 5$ m. The area of a triangle is $A_{\triangle}=\frac{1}{2}bh$. So, $A_{\triangle}=\frac{1}{2}\times8\times5=20$ m².

Step3: Calculate total area of triangular faces

There are 4 triangular faces. The total area of the triangular faces $A_{triangles}=4\times A_{\triangle}=4\times20 = 80$ 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, $A=A_{base}+A_{triangles}=64 + 80=144$ m².

Answer:

144