Question

find the surface area of the pyramid using the net. find the area of the square base. square base: ? cm² triangular sides: ? cm² total surface area: ? cm²

Explanation:

Step1: Calculate area of square base

The base is a square with side length \( 8 \, \text{cm} \). The formula for the area of a square is \( A = s^2 \), where \( s \) is the side length.
\( A_{\text{base}} = 8^2 = 64 \, \text{cm}^2 \)

Step2: Calculate area of one triangular face

Each triangular face has a base of \( 8 \, \text{cm} \) and a height of \( 8 \, \text{cm} \). The formula for the area of a triangle is \( A = \frac{1}{2}bh \), where \( b \) is the base and \( h \) is the height.
\( A_{\text{triangle}} = \frac{1}{2} \times 8 \times 8 = 32 \, \text{cm}^2 \)

Step3: Calculate total area of triangular faces

There are 4 triangular faces, so total area of triangles is \( 4 \times 32 = 128 \, \text{cm}^2 \)

Step4: Calculate total surface area

Total surface area is the sum of the area of the base and the total area of the triangular faces.
\( \text{Total Surface Area} = 64 + 128 = 192 \, \text{cm}^2 \)

Answer:

• Square base: \( 64 \, \text{cm}^2 \)
• Triangular sides: \( 128 \, \text{cm}^2 \)
• Total surface area: \( 192 \, \text{cm}^2 \)