What is the surface area of the triangular prism? 8cm, 10cm, 9cm, 6cm(1 point)
To calculate the surface area of a triangular prism, you need to find the areas of all the surfaces and then sum them up.
The formula for the surface area of a triangular prism is:
Surface Area = 2(Base Area) + (Lateral Area)
where Base Area = 1/2 * base * height of the triangle
Given that the base of the triangle is 8 cm and the height is 6 cm, the Base Area is:
Base Area = 1/2 * 8 * 6 = 24 cm²
Next, we need to find the lateral area of the prism. The lateral area of a triangular prism is equal to the area of the three rectangular faces.
The lateral area of the prism is the sum of the areas of the three rectangles:
Lateral Area = perimeter of the base * height of the prism
Perimeter of the base = 8 + 10 + 9 = 27 cm
Lateral Area = 27 * 6 = 162 cm²
Now we can calculate the total surface area of the triangular prism:
Surface Area = 2(24) + 162 = 48 + 162 = 210 cm²
Therefore, the surface area of the triangular prism with dimensions 8cm, 10cm, 9cm, and 6cm is 210 cm².
wrong
Apologies for the mistake. Let's recalculate the surface area of the triangular prism.
The triangular prism has two triangular faces and three rectangular faces.
1. Triangular faces:
Each triangular face has a base of 8 cm and a height of 6 cm.
Area of one triangular face = 1/2 * base * height = 1/2 * 8 * 6 = 24 cm²
Since there are two triangular faces, their total area is 2 * 24 = 48 cm²
2. Rectangular faces:
The three rectangular faces have dimensions:
- 8 cm x 10 cm (2 faces)
- 10 cm x 9 cm (1 face)
Area of one rectangular face = length x width
Area of two rectangular faces = 2 * (8 * 10) = 160 cm²
Area of one rectangular face = 10 * 9 = 90 cm²
Total area of the rectangular faces = 160 + 90 = 250 cm²
Now, calculate the total surface area by summing up the areas of the triangular and rectangular faces:
Total surface area = 48 (triangular faces) + 250 (rectangular faces) = 298 cm²
Therefore, the surface area of the triangular prism with dimensions 8cm, 10cm, 9cm, and 6cm is 298 cm².