Question

Find the surface area of the pyramid to the nearest whole number.

140 in2

40 in2,

180 in2

80 in2.

Answer 1

taking a peek at the pyramid, is really just 4 triangles stemming from a common top and touching a squarish base at the edges.

so hmmm to get the surface area of the pyramid, we can simply get the area of all those four triangles and the square and sum them up.

`\stackrel{\textit{\LARGE Areas}}{\stackrel{\textit{four triangles}}{4\left[\cfrac{1}{2}(\stackrel{b}{10})(\stackrel{h}{4}) \right]}~~ + ~~\stackrel{square}{(10)(10)}}\implies 80~~ + ~~100\implies 180~in^2`

Answer 2

The surface area of the pyramid is 180 in² to the nearest whole number.

Step 1: Calculate the area of the base.

The base of the pyramid is a rectangle with a length of 10 inches and a width of 10 inches. Therefore, the area of the base is:

Base area = length x width = 10 in x 10 in = 100 in²

Step 2: Calculate the area of each triangular face.

There are four triangular faces on the pyramid. Each triangle has a height of 4 inches and a base equal to the width of the base (10 inches). Therefore, the area of each triangular face is:

Triangle area = (1/2) * base * height = (1/2) * 10 in * 4 in = 20 in²

Step 3: Calculate the total surface area.

To find the total surface area, add the area of the base to the area of each triangular face:

Total surface area = Base area + 4 * Triangle area

Total surface area = 100 in² + 4 * 20 in²

Total surface area = 100 in² + 80 in²

Total surface area = 180 in²

Therefore, the surface area of the pyramid is 180 square inches to the nearest whole number.