What does the surface area of a figure measure?
Question 30 options:
1)
The area of the base.
2)
The area of the lateral faces.
3)
The area of the base and the lateral faces.
4)
The area of one base and one lateral face.
3 answers
3) The area of the base and the lateral faces.
What is the surface area of an equilateral triangular pyramid with a height of 4 inches and a base of 5 inches?
Question 29 options:
1)
10 units2
2)
40 units2
3)
60 units2
4)
80 units2
Question 29 options:
1)
10 units2
2)
40 units2
3)
60 units2
4)
80 units2
The surface area of an equilateral triangular pyramid is given by the formula:
SA = (1/2)bh + (3/2)B
where b is the base of the triangle, h is the height of the triangle, and B is the area of the base.
In this case, b = 5 inches, h = 4 inches, and the base is an equilateral triangle with side length 5 inches, so B = (sqrt(3)/4)b^2 = (sqrt(3)/4)5^2 = (sqrt(3)/4)25 = (5sqrt(3))/4 inches^2.
Plugging these values into the formula, we get:
SA = (1/2)(5)(4) + (3/2)(5sqrt(3))/4
SA = 10 + (15sqrt(3))/4
SA ≈ 23.66 inches^2
Therefore, the surface area of the triangular pyramid is approximately 23.66 square inches. The closest option is 2) 40 units2, but it is not exact.
SA = (1/2)bh + (3/2)B
where b is the base of the triangle, h is the height of the triangle, and B is the area of the base.
In this case, b = 5 inches, h = 4 inches, and the base is an equilateral triangle with side length 5 inches, so B = (sqrt(3)/4)b^2 = (sqrt(3)/4)5^2 = (sqrt(3)/4)25 = (5sqrt(3))/4 inches^2.
Plugging these values into the formula, we get:
SA = (1/2)(5)(4) + (3/2)(5sqrt(3))/4
SA = 10 + (15sqrt(3))/4
SA ≈ 23.66 inches^2
Therefore, the surface area of the triangular pyramid is approximately 23.66 square inches. The closest option is 2) 40 units2, but it is not exact.