The surface area of the triangular prism shown is 5,768 square units. Other dimensions are also shown on the net. What is the height of the prism?
(1 point)
dimensions are
7
25
and 24
The formula for the surface area of a triangular prism is:
SA = 2B + Ph
Where SA is the surface area, B is the area of the base, P is the perimeter of the base, and h is the height of the prism.
From the net, we can see that the base is a triangle with base 24 and height 7, so:
B = (1/2)(24)(7) = 84
The perimeter of the base is the sum of the three sides, which is:
P = 7 + 25 + 24 = 56
Substituting these values into the formula, we get:
5768 = 2(84) + 56h
Simplifying:
5768 = 168 + 56h
5600 = 56h
h = 100
Therefore, the height of the prism is 100 units.
are u surw
Yes, I'm sure.
like 100 units sure?
Yes, according to the given dimensions and surface area of the triangular prism, the height of the prism is 100 units.
To find the height of the triangular prism, we need to use the formula for the surface area of a triangular prism. The formula is:
Surface Area = 2 * (base area of the triangle) + (perimeter of the base triangle) * height
Looking at the given dimensions, we can see that the base of the triangular prism is a triangle with dimensions 7, 25, and 24.
First, let's find the base area of the triangle using Heron's formula. Heron's formula states that the area of a triangle with sides a, b, and c is given by:
Area = sqrt(s * (s-a) * (s-b) * (s-c))
where s is the semi-perimeter of the triangle, given by:
s = (a + b + c) / 2
Using these formulas, we can find the base area of the triangle:
s = (7 + 25 + 24)/2 = 56/2 = 28
Area = sqrt(28 * (28-7) * (28-25) * (28-24)) = sqrt(28 * 21 * 3 * 4) = sqrt(7056) = 84
Next, we can substitute the given values into the surface area formula:
5768 = 2 * 84 + (7 + 25 + 24) * height
5768 = 168 + 56 * height
5768 - 168 = 56 * height
5600 = 56 * height
Finally, we can solve for the height by dividing both sides of the equation by 56:
height = 5600 / 56 = 100 units
Therefore, the height of the prism is 100 units.