Question

Find the surface area of the square pyramid, Show your work please : )

Answer 1

Answer:

105 in.

Step-by-step explanation:

To find the area of a square pyramid, use this formula

a (area of base) + 1/2 ⋅ p (perimeter of base) ⋅ height.

The base is a square.

To find the area of a square, simply multiply the side length by itself twice (x^2).

5 x 5 = 25.

25 is the area of the base.

a (area of base) + 1/2 ⋅ p (perimeter of base) ⋅ height

25 + 1/2 ⋅ p ⋅ height.

To find the perimeter of a square, add every side length; the sum is the perimeter.

5 + 5 + 5 + 5 = 20.

20 is the perimeter of the square.

a (area of base) + 1/2 ⋅ p (perimeter of base) ⋅ height

25 + 1/2 ⋅ 20 ⋅ height

The height is the number along the little lines.

8 is the height.

Now that we have all parts of the formula, we have our final equation.

a (area of base) + 1/2 ⋅ p (perimeter of base) ⋅ height

25 + 1/2 ⋅ 20 ⋅ 8 = 105.

105 in. is the surface area of the square pyramid.

Answer 2

Answer:

105in²

Step-by-step explanation:

Surface area is the total area of the faces.

The faces of pyramid consist of triangles and a square

The area of a square can easily be calculated by squaring the side length

the square of this pyramid has a side length of 5

so

area of square = 5²

5² = 25

the area of the square is 25in²

Now to find the area of the triangles

All we have to do is find the area of one triangle and multiply that buy 4 ( because there are four triangle)

the area of a triangle can be calculated using this formula :

$A=\frac{bh}{2}$  where b = base and h = height

The triangles have a base length of 5 in and a height of 8 in

so

$A=\frac{5*8}{2} \\5*8=40\\\frac{40}{2} =20\\A=20$

So the area of one triangle is 20 in²

Now we multiply 20 by 4 to find the area of all 4 triangles

20 * 4 = 80

So the total area of the triangles is 80in²

Finally we add the two areas together

Surface area = 80 + 25

80 + 25 = 105

Hence, the surface area is 105in²