What is the surface area of the triangular prism?
the image has a trianglular prism with the height 8 cm the width of 6 cm the base of 9 and the length of 10 find the surface area
To calculate the surface area of a triangular prism, you need to find the areas of all the individual faces and then sum them up.
1. Find the area of the two triangular faces:
- The area of a triangle is given by the formula: 0.5 * base * height
- Let's say the base of the triangle is 10 units and the height is 5 units
- Area of one triangle = 0.5 * 10 * 5 = 25 square units
- Since there are two triangular faces, the total area of both triangles = 2 * 25 = 50 square units
2. Find the area of the three rectangular faces:
- The area of a rectangle is given by the formula: length * width
- Let's say the length of the rectangle is 10 units, the width at the base of the triangles is 5 units, and the width at the top of the triangles is 3 units
- Area of the three rectangles = 10 * 5 + 10 * 3 + 5 * 3 = 50 + 30 + 15 = 95 square units
3. Add the areas of all faces to find the total surface area:
Total surface area = 50 + 95 = 145 square units
Therefore, the surface area of the triangular prism is 145 square units.
To find the surface area of the triangular prism, we need to calculate the areas of all the individual faces and then sum them up.
1. Find the area of the two triangular faces:
- The formula for the area of a triangle is 0.5 * base * height.
- Since the base of the triangles is 9 cm and the height is 8 cm, the area of each triangle is 0.5 * 9 * 8 = 36 square cm.
- Since there are two triangular faces, the total area of both triangles is 2 * 36 = 72 square cm.
2. Find the area of the three rectangular faces:
- The formula for the area of a rectangle is length * width.
- The length of the rectangular faces is 10 cm and the width varies.
- The width of one rectangle is 6 cm, resulting in an area of 10 * 6 = 60 square cm.
- The width of the other two rectangles is 9 cm, resulting in areas of 10 * 9 = 90 square cm (each).
- The total area of the three rectangular faces is 60 + 90 + 90 = 240 square cm.
3. Add the areas of all faces to find the total surface area:
Total surface area = 72 (triangular faces) + 240 (rectangular faces) = 312 square cm.
Therefore, the surface area of the triangular prism is 312 square cm.