Find The Surface Area Of The Regular Pyramid. Round Your Answer To The Nearest Tenth (One Decimal Place). SA=B+0.5p/ 2 Ft SA= _ Blank 1: Question 2 (1 Point) Find The Surface Area Of The Regular Pyramid. Round Your Answer To The Nearest Tenth (One Decimal Place). SA = B +0.5p/ SA = Cma Blank 1: Question 3 (1 Point) Find The Surface
The Correct Answer and Explanation is :
To find the surface area ((SA)) of a regular pyramid, the formula is:
[
SA = B + \frac{1}{2}P \cdot l
]
Where:
- (B) is the area of the base.
- (P) is the perimeter of the base.
- (l) is the slant height of the pyramid.
Step-by-Step Process:
- Identify Base Area ((B)):
Calculate the area of the base using its shape. For example:
- If the base is a square with side length (s), then (B = s^2).
- If the base is a triangle, use (B = \frac{1}{2} \cdot \text{base} \cdot \text{height}).
- Find Perimeter ((P)):
Calculate the total perimeter of the base. For example:
- For a square base with side length (s), (P = 4s).
- For a triangle, add up all side lengths.
- Determine Slant Height ((l)):
The slant height is typically given or can be found using the Pythagorean theorem if the pyramid height ((h)) and half the base diagonal are known. - Substitute Values into the Formula:
Plug the values of (B), (P), and (l) into the formula and calculate the surface area.
Example Problem:
A square pyramid has a base side length of (4 \, \text{ft}) and a slant height of (5 \, \text{ft}).
- Base Area ((B)):
(B = s^2 = 4^2 = 16 \, \text{ft}^2). - Perimeter ((P)):
(P = 4s = 4 \cdot 4 = 16 \, \text{ft}). - Surface Area ((SA)):
[
SA = B + \frac{1}{2}P \cdot l
]
Substitute (B = 16), (P = 16), and (l = 5):
[
SA = 16 + \frac{1}{2}(16 \cdot 5) = 16 + \frac{1}{2}(80) = 16 + 40 = 56 \, \text{ft}^2
]
Final Answer:
The surface area is (56 \, \text{ft}^2).