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) 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
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.
To determine what the surface area of a figure measures, we should understand the concept of surface area. The surface area is the total area of all the faces of a three-dimensional figure. It helps us determine how much material we would need to cover the entire figure if we were to wrap it.
Now, let's consider the options provided:
1) The area of the base: This option only considers the area of the base of the figure. However, the surface area includes all the faces, not just the base, so this option is not correct.
2) The area of the lateral faces: This option only considers the area of the lateral faces, which are the sides of the figure. However, the surface area also includes the base, so this option is not correct.
3) The area of the base and the lateral faces: This option correctly identifies that the surface area includes both the area of the base and the area of the lateral faces. This is because the surface area is the sum of all the areas of the faces.
4) The area of one base and one lateral face: This option only includes the area of one base and one lateral face. However, the surface area includes all the faces, so this option is not correct.
Therefore, the correct answer is option 3) The area of the base and the lateral faces.