ANSWER
The perimeter of the base = 40 ft
The slant height = 13 ft
L.A = 260 ft^2
Area of a base = 100 ft^2
S.A = 360 ft^2
EXPLANATION
Given information
The figure given is a square-based pyramid
The base side of the pyramid = 10 ft
The slant height of the pyramid = 13 ft
Firstly, we need to find the perimeter of a square-based pyramid
The formula for calculating the perimeter of a square-based pyramid is given below as
[tex]\begin{gathered} \text{ Perimeter = 4a} \\ \text{ a= 10ft} \\ \text{ Perimeter = 4}\times10 \\ \text{ Perimeter = 40.0ft} \end{gathered}[/tex]
Part B
The slant height of the pyramid is 13 ft
Part C
Find the lateral area of the pyramid?
To find the lateral area of the pyramid, follow the steps below
Step 1: Write the formula for calculating the lateral area of the pyramid
[tex]\begin{gathered} \text{ L.A = 2al when slant height\lparen l\rparen is given} \\ \text{ Where a is the base side of the pyramd and l is the slant height of the pyramid} \end{gathered}[/tex]Substitute a =10 and h = 13 into the above formula in step 1
[tex]\begin{gathered} \text{ L.A = 2 }\times\text{ 10}\times13 \\ \text{ L.A = 2}\times130 \\ \text{ L.A = 260.0 ft}^2 \end{gathered}[/tex]Part D
Find the area of base of the pyramid
The formula for calculating the area of the base of the pyramid is given below as
[tex]\text{ Base area of the pyramid = a}^2[/tex]a = 10 ft
[tex]\begin{gathered} \text{ Base area of the square-base pyramid = 10}^2 \\ \text{ Base area of the square-based pyramid = 100 ft}^2 \end{gathered}[/tex]Part E
[tex]\begin{gathered} \text{ Surface area = a}^2\text{ + 2al} \\ \text{ where l is the slant height and a is the base side of the pyramid} \end{gathered}[/tex][tex]\begin{gathered} \text{ Surface area of the pyramid = 10}^2\text{ + 2 }\times13\times10 \\ \text{ Surface area of the pyramid = 100 + 260} \\ \text{ Surface area of the pyramid = 360 ft}^2 \end{gathered}[/tex]
