Question

1. here is the net of a square - based pyramid. what is the surface area of the polyhedron (3d shape)? 5 cm 5 cm 8 cm

Explanation:

Step1: Calculate base - area

The base is a square with side length $s = 5$ cm. The area of a square is $A_{base}=s^{2}$. So, $A_{base}=5^{2}=25$ $cm^{2}$.

Step2: Calculate area of one triangular face

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

Step3: Calculate total area of triangular faces

There are 4 triangular faces. The total area of the triangular faces is $A_{triangles}=4\times A_{triangle}=4\times20 = 80$ $cm^{2}$.

Step4: Calculate surface - area of the pyramid

The surface - area $A$ of the square - based pyramid is the sum of the base area and the total area of the triangular faces. So, $A=A_{base}+A_{triangles}=25 + 80=105$ $cm^{2}$.

Answer:

$105$ $cm^{2}$