Question

Henrique drew and labeled the net shown. He also labeled the areas of the left and right triangular sides.

A net has a rectangle at the center and 4 triangles on the sides. The rectangle has a length of 10 inches and height of 4 inches. 2 triangles have a base of 10 inches and a height of 5 inches. The other 2 triangles have an area of 13.6 inches squared.

Use Henrique’s work and finish finding the areas of the faces.

What is the surface area of the rectangular pyramid?

in.2

Answer 1

117.2 is the answer

Answer 2

Answer:
`SA=117.2\ in^2`

Explanation:

You need to remember the following:

1. The area of a rectangle can be calculated with the following formula:

`A_r=lw`

Where "l" is the length and "w" is the width.

2. The area of a triangle can be calculated with the following formula:

`A_t=(bh)/(2)`

Where "b" is the base and "h" is the height.

Use those formulas to find the area of each face.

Area of the rectangle

`A_r=(10\ in)(4\ in)=40\ in^2`

Area of two triangles

There are two equal triangles. Each one has a base of 10 inches and a height of 5 inches. Then, their areas are equal:

`A_(t1)=A_(t2)=((10\ in)(5\ in))/(2)=25\ in^2`

The areas of the other two triangles (which are equal) are:

`A_(t3)=A_(t4)=13.6\ in^2`

Adding the areas of the faces, you get that the surface area of the rectangular pyramid is:

`SA=40\ in^2+25\ in^2+25\ in^2+13.6\ in^2+13.6\ in^2\\\\SA=117.2\ in^2`