Question

find the surface area of the pyramid using the net. 10 cm (arrow to triangles height), 6 cm (square side). 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 \( s = 6 \, \text{cm} \). The formula for the area of a square is \( A = s^2 \).
\( A_{\text{base}} = 6^2 = 36 \, \text{cm}^2 \)

Step2: Calculate area of one triangular face

Each triangular face has a base of \( 6 \, \text{cm} \) and a height of \( 10 \, \text{cm} \). The formula for the area of a triangle is \( A = \frac{1}{2} \times \text{base} \times \text{height} \).
\( A_{\text{triangle}} = \frac{1}{2} \times 6 \times 10 = 30 \, \text{cm}^2 \)

Step3: Calculate total area of triangular faces

There are 4 triangular faces. So total area of triangles is \( 4 \times A_{\text{triangle}} \).
\( A_{\text{triangles total}} = 4 \times 30 = 120 \, \text{cm}^2 \)

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.
\( \text{Total Surface Area} = A_{\text{base}} + A_{\text{triangles total}} = 36 + 120 = 156 \, \text{cm}^2 \)

Answer:

s:
Square Base: \( \boldsymbol{36} \, \text{cm}^2 \)
Triangular sides: \( \boldsymbol{120} \, \text{cm}^2 \)
Total surface area: \( \boldsymbol{156} \, \text{cm}^2 \)