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
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