What is the surface area of right triangular prism with a height of 20 units and a base with legs of length 3 units and 4 units and a hypotenuse of length 5 units
[(3 + 4 + 5) * 20] + (3*4) = ?
area of base = (1/2)(3)(4)
area of top = (1/2)(3)(4)
area of sides = 20 * ( 3 + 4 + 5 )
To find the surface area of a right triangular prism, we can break it down into three parts: the two triangular bases and the three rectangular faces.
1. Triangular bases:
The area of a triangle can be calculated using the formula A = 1/2 * base * height. In this case, the base and height of the triangles are the lengths of their legs. For the first triangular base, the legs measure 3 units and 4 units, so its area would be A = 1/2 * 3 * 4. For the second triangular base, the legs have the same lengths, so the area would also be A = 1/2 * 3 * 4. Therefore, the combined area of the triangular bases is 1/2 * 3 * 4 + 1/2 * 3 * 4.
2. Rectangular faces:
To find the area of a rectangle, we multiply its length by its width. In this case, the length of the rectangular faces is the height of the prism, which is 20 units. The width is the perimeter of the triangular base, excluding the hypotenuse. The perimeter of a triangle is the sum of the lengths of its sides. For the triangular base given, the perimeter is 3 + 4 + 5. So the area of each rectangular face would be 20 * (3 + 4 + 5). Since there are three rectangular faces, the combined area would be 3 * (20 * (3 + 4 + 5)).
To calculate the total surface area, we add the area of the triangular bases to the combined area of the rectangular faces.
Area of triangular bases: (1/2 * 3 * 4) + (1/2 * 3 * 4)
Area of rectangular faces: 3 * (20 * (3 + 4 + 5))
Total surface area = Area of triangular bases + Area of rectangular faces