Question

here is a square pyramid and its net. the lateral faces are congruent triangles. the base (shaded) is a square. (all lengths are in centimeters.) (a) find the area of the base of the pyramid. 9 cm² (b) find the area of one lateral face of the pyramid. 3.45 cm² (c) use the net to find the lateral surface area of the pyramid. 2 cm² (d) use the net to find the total surface area of the pyramid. 2 cm²

Explanation:

Step1: Identify the base shape

The base is a square with side length \( 3 \) cm (from the net diagram, the square has side \( 3 \) cm).

Step2: Calculate the area of the square base

The formula for the area of a square is \( A = s^2 \), where \( s \) is the side length. Substituting \( s = 3 \) cm, we get \( A = 3^2 = 9 \) \( \text{cm}^2 \).

Answer:

\( 9 \) square centimeters (for part (a))

For part (b):

Step1: Identify the lateral face shape

Each lateral face is a triangle. The base of each triangle is the side of the square base, so \( b = 3 \) cm. The height (altitude) of each triangle is given as \( 2.3 \) cm (from the net diagram).

Step2: Calculate the area of one triangular face

The formula for the area of a triangle is \( A = \frac{1}{2} \times b \times h \). Substituting \( b = 3 \) cm and \( h = 2.3 \) cm, we get \( A = \frac{1}{2} \times 3 \times 2.3 = 3.45 \) \( \text{cm}^2 \).