Question

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A rectangular pyramid. The rectangular base has a length of 10 inches and a width of 6 inches. 2 triangular sides have a base of 10 inches and height of 5.6 inches. 2 triangular sides have a base of 5 inches and height of 7.1 inches.

The base of the rectangular pyramid shown has an area of ___ square inches

A triangular face with a base of 10 inches has an area of ___ square inches.

A triangular face with a base of 5 inches has an area of ___ square inches.

The total surface area of the pyramid is ___ square inches.

Answer 1

`A_(b) = 60\,in^(2)`,
`A_(s,I) = 28\,in^(2)`,
`A_(s,II) = 17.75\,in^(2)`,
`A_(T) = 151.5\,in^(2)`

Explanation:

The base of the rectangular pyramid has an area of:

`A_(b) = (10\,in)\cdot (6\,in)`

`A_(b) = 60\,in^(2)`

The triangular face with a base of 10 inches has an area of:

`A_(s,I) = (1)/(2)\cdot (10\,in)\cdot (5.6\,in)`

`A_(s,I) = 28\,in^(2)`

The triangular face with a base of 5 inches has an area of:

`A_(s,II) =(1)/(2)\cdot (5\,in)\cdot (7.1\,in)`

`A_(s,II) = 17.75\,in^(2)`

The total surface area of the pyramid is:

`A_(T) = A_(b) + 2\cdot (A_(s,I)+A_(s,II))`

`A_(T) = 60\,in^(2) + 2\cdot (28\,in^(2)+17.75\,in^(2))`

`A_(T) = 151.5\,in^(2)`

Answer 2

a) The base of the rectangular pyramid shown has an area of

60 square inches

b) A triangular face with a base of 10 inches has an area of 28 square inches.

c) A triangular face with a base of 5 inches has an area of 17.75 square inches.

d) The total surface area of the pyramid is 151.5 square inches.

Explanation:

a) Solving for question a, we were given the following parameters

A rectangular pyramid. The rectangular base has a length of 10 inches and a width of 6 inches

The formula used to calculate the rectangular base of a rectangular pyramid =

Length × Width

Where :

Length = 10 inches

Width = 6 inches

Rectangular base = 10 inches × 6 inches

= 60 inches²

Hence, the base of the rectangular pyramid shown has an area of 60 square inches

b) Solving for question b, we have the following values given:

2 triangular sides have a base of 10 inches and height of 5.6 inches.

First step would be to solve for one triangular side first.

The area of the one triangular side = (Base × Height) ÷ 2

= (10 inches × 5.6 inches) ÷ 2

= 56inches² ÷ 2

= 28 inches²

Therefore, for the 2 triangular sides, since they have the same base and height, the other side as well would be 28 inches².

A triangular face with a base of 10 inches has an area of 28 square inches.

c) Solving for question c, the following parameters are given:

2 triangular sides have a base of 5 inches and height of 7.1 inches.

We would be to solving for one triangular side first.

The area of the one triangular side = (Base × Height) ÷ 2

= (5 inches × 7.1 inches) ÷ 2

= 35.5 inches² ÷ 2

= 17.75 inches²

Therefore, for the 2 triangular sides, since they have the same base and height, the other side as well would be 17.75 inches².

A triangular face with a base of 5 inches has an area of 17.75 square inches.

d) Solving for d, it is important to note that, a rectangular pyramid has 5 faces and they are: The rectangular base and 4 triangular faces

The formula for the total surface area of the rectangular pyramid is given as

Total Surface Area of the rectangular pyramid = Rectangular Base + Area of Triangular Side A + Area of Triangular Side B + Area of Triangular Side C + Area of Triangular Side D + Area of Triangular Side E

Total Surface Area of the Rectangular Pyramid = 60 inches² + 28 inches² + 28 inches² + 17.75 inches² + 17.75 inches²

Total surface Area of the Rectangular pyramid = 151.5 inches²

The total surface area of the pyramid is 151.5 square inches.