Final answer:
The total surface area of the regular pyramid is 241.8 sq cm, obtained by adding the base area (84.3 sq cm) to the total area of the five triangles (157.5 sq cm).
Step-by-step explanation:
We need to find the surface area of a regular pyramid with a pentagonal base. The base area is already given, which is 84.3 sq cm. Since it's a pyramid with a pentagonal base, there are five triangular faces. To find the area of each triangle, we use the formula for the area of a triangle A=1/2 × base × height. The base of each triangle is 7 cm, and the height is 9 cm.
To calculate the area of one triangle, perform the following calculation: A=1/2 × 7 cm × 9 cm = 31.5 cm². Given there are five identical triangles, we then multiply this area by 5 to find the total surface area of all triangular sides: 31.5 cm² × 5 = 157.5 cm².
To find the total surface area of the pyramid, we add the area of the pentagonal base to the total area of the triangular sides: 84.3 cm² + 157.5 cm² = 241.8 cm².