Surface Area of Triangular Prisms Quick Check 1 of 51 of 5 Items Question What is a two-dimensional representation of a three-dimensional figure?(1 point) Responses a rectangle a rectangle a triangular prism a triangular prism a net a net a triangle
Answers 8, 16, 10, 17
a net
What is the missing length l of the triangular prism if the surface area is 524 square centimeters?
To find the missing length of the triangular prism, we need to know the formula for calculating the surface area of a triangular prism.
The formula for the surface area of a triangular prism is:
Surface Area = 2 * Base Area + Lateral Area
Base Area = (1/2) * base * height
Lateral Area = perimeter of base * height
Given that the surface area of the triangular prism is 524 square centimeters, we also need the base length, base height, height of the prism, and the perimeter of the base.
If you provide the information about the dimensions of the triangular prism, we can calculate the missing length "l".
What is the missing length l of the triangular prism if the surface area is 524 square centimeters? 8,16,17,10 are the answers
To find the missing length "l" of the triangular prism, we need the formula for the surface area of a triangular prism and the dimensions of the prism.
The formula for the surface area of a triangular prism is:
Surface Area = 2 * Base Area + Lateral Area
Given that the surface area of the triangular prism is 524 square centimeters, we need to find the missing length "l" - one of the dimensions of the prism.
Without additional information about the dimensions of the triangular prism, we cannot calculate the missing length. Could you provide the dimensions of the base and height of the prism so we can solve for the missing length?
height 10 cm
Given that the height of the triangular prism is 10 cm and the surface area is 524 square centimeters, we can calculate the missing length "l" using the formula for the surface area of a triangular prism:
Surface Area = 2 * Base Area + Lateral Area
Since the base of a triangular prism is a triangle, the Base Area = (1/2) * base * height
Let's assume the base of the triangle has sides of length "a", "b", and "c" where "a" and "b" are the base and height respectively. The perimeter of the base, c, can be calculated as c = a + b + c.
Since the surface area is given as 524 square centimeters and the height is 10 cm, we can set up an equation to solve for the missing length "l":
524 = 2 * (1/2) * base * 10 + (perimeter of base) * 10
524 = base * 10 + c * 10
Since c = a + b + l and a = b (due to triangular base), we get:
base + base + l = perimeter
2 * base + l = perimeter
Now, we need additional information about the base (side lengths) of the triangular prism to find the missing length "l". Once we have that information, we can substitute the values into the equations to solve for "l".
base is 6cm
Given that the height of the triangular prism is 10 cm and the base length is 6 cm, we can now calculate the missing length "l" using the formula for the surface area of a triangular prism:
Surface Area = 2 * Base Area + Lateral Area
First, calculate the base area:
Base Area = (1/2) * base * height
Base Area = (1/2) * 6 cm * 10 cm
Base Area = 30 square cm
Since the base is a triangle, the perimeter of the base would be:
Perimeter of base = 6 cm + 6 cm + l
Perimeter of base = 12 cm + l
Then, calculate the missing length "l" using the surface area formula:
524 sq cm = 2 * 30 sq cm + (12 cm + l) * 10 cm
524 sq cm = 60 sq cm + 120 cm + 10l
524 sq cm = 60 sq cm + 120 cm + 10l
524 sq cm = 180 sq cm + 10l
10l = 524 sq cm - 180 sq cm
10l = 344 sq cm
l = 344 sq cm / 10
l = 34.4 cm
Therefore, the missing length "l" of the triangular prism is approximately 34.4 cm.