To find the total surface area of the 3-D figure, we need to calculate the surface area of each face and then add them together.
Given measurements:
- Base of figure: 20 m by 12 m
- Height of figure (perpendicular to the base): 8 m
- Sides of the figure: 10 m and 32 m
Step 1: Calculate the surface area of the base (20 m by 12 m):
Base Surface Area = Length x Width
Base Surface Area = 20 m x 12 m
Base Surface Area = 240 square meters
Step 2: Calculate the surface area of the side facing 20 m (rectangular face):
Side Surface Area = Length x Height
Side Surface Area = 20 m x 8 m
Side Surface Area = 160 square meters
Step 3: Calculate the surface area of the side facing 12 m (rectangular face):
Side Surface Area = Width x Height
Side Surface Area = 12 m x 8 m
Side Surface Area = 96 square meters
Step 4: Calculate the surface area of the triangle face with sides 10 m, 20 m, and 22 m. We will use Heron's formula to calculate the area of the triangle.
Semi-perimeter (s) = (10 m + 20 m + 32 m) / 2
s = 31 m
Area (A) = √[s(s-10)(s-20)(s-32)]
A = √[31(31-10)(31-20)(31-32)]
A ≈ 172.9 square meters
Step 5: Calculate the total surface area by adding all the individual surface areas:
Total Surface Area = Base Area + 2(Side Area) + Triangle Area
Total Surface Area = 240 square meters + 2(160 square meters + 96 square meters) + 172.9 square meters
Total Surface Area ≈ 824.90 square meters
Therefore, the total surface area of the 3-D figure is approximately 824.90 square meters.
What is the total surface area of the 3-D figure with the measurements of 20 m 12 m 8 m 10 m and 32 m
1 answer