Answer:
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.
Step-by-step 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.
Answer:
[tex]A_{b} = 60\,in^{2}[/tex], [tex]A_{s,I} = 28\,in^{2}[/tex], [tex]A_{s,II} = 17.75\,in^{2}[/tex], [tex]A_{T} = 151.5\,in^{2}[/tex]
Step-by-step explanation:
The base of the rectangular pyramid has an area of:
[tex]A_{b} = (10\,in)\cdot (6\,in)[/tex]
[tex]A_{b} = 60\,in^{2}[/tex]
The triangular face with a base of 10 inches has an area of:
[tex]A_{s,I} = \frac{1}{2}\cdot (10\,in)\cdot (5.6\,in)[/tex]
[tex]A_{s,I} = 28\,in^{2}[/tex]
The triangular face with a base of 5 inches has an area of:
[tex]A_{s,II} =\frac{1}{2}\cdot (5\,in)\cdot (7.1\,in)[/tex]
[tex]A_{s,II} = 17.75\,in^{2}[/tex]
The total surface area of the pyramid is:
[tex]A_{T} = A_{b} + 2\cdot (A_{s,I}+A_{s,II})[/tex]
[tex]A_{T} = 60\,in^{2} + 2\cdot (28\,in^{2}+17.75\,in^{2})[/tex]
[tex]A_{T} = 151.5\,in^{2}[/tex]
