Question

Find the volume of a right-angled triangle based prism whose sides of the base are 3m, 4m, 5m and height is 8m.

Answer 1

Hint: We first try to define the concept of a right-angled triangle-based prism where we formulate the volume of the prism as the multiplication of the height of the prism and area of the base. Then we find the area of the base of the prism which has sides of the base as 3m, 4m, 5m. Then using the height multiplication, we find the volume.

Complete step by step answer:
In the case of a right-angled triangle-based prism, the formula pf volume of the prism is equal to the multiplication of the height of the prism and area of the base.
So, we first find the area of the base of the prism which has sides of the base as 3m, 4m, 5m.
As the base right-angled triangle, the area will be half of the multiple of the lengths of the arms of the right angle.
So, the area of the base is $ \dfrac{1}{2}\times 3\times 4=6\text{ }{{\text{m}}^{2}} $ . We understood the sides are 3 and 4 as the hypotenuse is the longest side of right-angled triangle.
The height of the right-angled triangle-based prism is 8m.
So, the volume of the prism is $ 6\times 8=48\text{ }{{\text{m}}^{3}} $ .
Therefore, the volume of a right-angled triangle-based prism whose sides of the base are 3m, 4m, 5m, and height is 8m is $ 48\text{ }{{\text{m}}^{3}} $ .

Note:
We need to remember this formula of the prism is only possible for regular prisms which particular bases. For other cases, we have to apply the concept of differential and we need more given information on that to find the volume.