Question

graham joined two congruent square pyramids to form the composite solid. not drawn to scale if the lateral faces of the pyramids each have an area of 18.4 cm², what is the total surface area of the composite solid? 158.2 cm² 147.2 cm² 73.6 cm² 110.4 cm²

Explanation:

Step1: Determine the number of lateral faces

A square pyramid has 4 lateral faces. Since there are 2 congruent square pyramids, the total number of lateral faces is \(4\times2 = 8\).

Step2: Calculate the total surface area

Given that the area of each lateral face is \(18.4\space cm^{2}\). The total surface area \(S\) of the composite solid (we don't consider the joined - together base as it is internal) is \(S=18.4\times8\).

$$S = 18.4\times8=(18 + 0.4)\times8=18\times8+0.4\times8=144+3.2 = 147.2\space cm^{2}$$

Answer:

\(147.2\space cm^{2}\)