Question

Hi I need a lot of help with this one thank u! The last number is 13 on top

Answer 1

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

Step-by-step 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

`\begin{gathered} \text{ Perimeter = 4a} \\ \text{ a= 10ft} \\ \text{ Perimeter = 4}*10 \\ \text{ Perimeter = 40.0ft} \end{gathered}`

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

`\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}`

Substitute a =10 and h = 13 into the above formula in step 1

`\begin{gathered} \text{ L.A = 2 }*\text{ 10}*13 \\ \text{ L.A = 2}*130 \\ \text{ L.A = 260.0 ft}^2 \end{gathered}`

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

`\text{ Base area of the pyramid = a}^2`

a = 10 ft

`\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}`

Part E

`\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}`
`\begin{gathered} \text{ Surface area of the pyramid = 10}^2\text{ + 2 }*13*10 \\ \text{ Surface area of the pyramid = 100 + 260} \\ \text{ Surface area of the pyramid = 360 ft}^2 \end{gathered}`