Question

What is the surface area of the pyramid shown to the nearest whole number? the diagram is not drawn to scale

A 56ft^2
B 72 ft^2
C 22 ft^2
D 128 ft^2

Answer 1

B 72 ft^2

Explanation:

The area surface of a square pyramid is given by adding the area of the square that creates the base, and then the area of the 4 triangles that make up for the sides of the pyramid, so we first calculate the area of the triangle:

Area= b*h/2

Area= 4*7/2

Area=14

Now we calculate the area of the base:

Area=side*side

Area=4*4

Area=16

No we add up the four triangles plus the base:

Surface area=(Sides*4)+base

Surface area= (14*4)+16

Surface area=56+16

Surface area=72

So the surface area of the pyramid would be 72 ft^2

Answer 2

(B)
`SA=72{\tex{feet^2}`

Explanation:

Given: From the figure, it is given that the length of the base is 4 feet and slant height is 7 feet.

To find: The Surface are of Pyramid.

Solution: From the figure, it is given that the length of the base is 4 feet and slant height is 7 feet.

Now, surface area of the Pyramid is given as:

`SA={\text{Area of base}+(1)/(2)pl`

where p is the perimeter and l is the slant height.

Now, area of base is given as:

`A=4(4){\tex{ft^2}`

`A=16{\tex{ft^2}`

And, the surface area is given as:

`SA=16+(1)/(2)(4)(4)(7)`

`SA=16+56`

`SA=72{\tex{feet^2}`

Hence, option B is correct.