Graham joined two congruent square pyramids to form the composite solid. 2 square pyramids are connected at their base. [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? 73.6 cm2 110.4 cm2 147.2 cm2 158.2 cm2

Question:

Graham joined two congruent square pyramids to form the composite solid. 2 square pyramids are connected at their base. [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?

a) 73.6 cm²

b) 110.4 cm²

c) 147.2 cm²

d) 158.2 cm²

Answer:

c) 147.2 cm²

Step-by-step explanation:

We are told in the question that two congruent square pyramids are connected at their base to form a composite solid.

It is important to note that a square pyramid has 4 lateral faces and one base. When two congruent square pyramids are connected at their base to form a composite solid, the total number of lateral faces of the composite solid = 8 lateral faces.

To calculate the total surface area of the composite solid = Sum of the area of Lateral faces of the pyramid.

In the question we are given the area of each of the faces of the lateral pyramid as 18.4cm². Since we have 8 lateral faces for the composite solid,

The total surface area of the composite solid = (18.4 cm² * 8)

= 147.2 cm²

Or 18.4 cm² + 18.4 cm² + 18.4 cm² + 18.4 cm² + 18.4 cm² + 18.4 cm² + 18.4 cm² + 18.4 cm²

= 147.2 cm²