1. Anna is making a sculpture in the shape of a triangular prism. The triangular bases have sides of length 10 m, 10 m , and 12 m and height of 8 m. She wants to coat the sculpture in a special finish that will preserve it longer. If the sculpture is 5 m thick, what is the total area she will have to cover with the finish ?
48 m
96 m
256 m
480 m
@mathhelper great job solving in but the answer is 256 so you might want to relook your work.
To find the total surface area of the sculpture, we need to consider the area of the two triangular bases and the area of the three rectangular faces.
The area of one triangular base can be calculated using the formula for the area of a triangle:
Area of a triangle = (base * height) / 2
Given that the sides of the triangle are 10 m, 10 m, and 12 m, and the height is 8 m, we can calculate:
Area of one triangular base = (10 * 8) / 2 = 40 m²
Since there are two triangular bases, the total area of the triangular bases is:
Total area of triangular bases = 2 * 40 m² = 80 m²
Next, we need to calculate the area of the three rectangular faces. Since the sculpture is 5 m thick, each rectangular face has a length equal to the perimeter of the triangle and a width of 5 m.
The perimeter of a triangle can be calculated by adding the lengths of its sides:
Perimeter of the triangle = 10 m + 10 m + 12 m = 32 m
Therefore, the area of each rectangular face is:
Area of a rectangular face = length * width = 32 m * 5 m = 160 m²
Since there are three rectangular faces, the total area of the rectangular faces is:
Total area of rectangular faces = 3 * 160 m² = 480 m²
Finally, to find the total area she will have to cover with the finish, we sum the areas of the triangular bases and the rectangular faces:
Total area = Total area of triangular bases + Total area of rectangular faces
Total area = 80 m² + 480 m² = 560 m²
Therefore, Anna will have to cover a total area of 560 m² with the special finish.
To find the total area that Anna will have to cover with the special finish, we need to calculate the surface area of the triangular prism.
A triangular prism has three rectangular faces and two triangular bases. To find the surface area, we need to calculate the area of each face and base and then add them together.
1) Find the area of one of the triangular bases:
The formula for the area of a triangle is: A = (1/2) * base * height.
Here, the base is 10 m, and the height is 8 m. So, the area of one triangular base is (1/2) * 10 m * 8 m = 40 m².
2) Find the area of one of the rectangular faces:
The formula for the area of a rectangle is: A = length * width.
The length of the rectangular face is the height of the triangular base, which is 8 m. The width of the rectangular face is the thickness of the sculpture, which is 5 m. So, the area of one rectangular face is 8 m * 5 m = 40 m².
3) Calculate the total area of the triangular bases: Since there are two triangular bases, the total area of the triangular bases is 2 * 40 m² = 80 m².
4) Calculate the total area of the rectangular faces: Since there are three rectangular faces, the total area of the rectangular faces is 3 * 40 m² = 120 m².
5) Add the areas of the triangular bases and rectangular faces together to find the total surface area: 80 m² + 120 m² = 200 m².
Therefore, Anna will have to cover a total area of 200 m² with the special finish.
This question is just as confusing now as when you posted it earlier.
First of all that is one huge sculpture!
None of your choices are in square metres.
Its surface area consists of 2 congruent isosceles triangles and 3 rectangles
The rectangles are 10*8 + 10*8 + 12*8
= 256 m^2
For the base we need the height with 12 as its base
By Pythagoras, h^2 + 6^2 = 10^2
h = 8
So the area of one triangle = (1/2)(base)(height)
= (1/2)(12)(8) = 48
so the area of the two triangles is 96 m^2 for a total of
256 + 96 or 352 m^2 , not one of the choices.
I have no clue what it meant by "the sculpture is 5 m thick means"
Curious to know what kind of textbooks Connexus uses.