A block of wood has a shape of a triangular prism and the bases are right triangles find is lateral area and surface area
Without knowing the dimensions of the block, we can still solve for the lateral area and surface area in terms of the base lengths and height of the right triangle.
Let's say the base of the right triangle is b, the height of the right triangle is h, and the height of the prism (perpendicular to the base) is L.
The lateral area refers to the total area of the non-base faces of the prism. Since this is a right triangular prism, there are three rectangular faces. Two of these faces are congruent and have dimensions of L by h (height by width). The third rectangular face has dimensions of L by b (height by length of base). Therefore, the lateral area is:
Lateral area = 2(Lh) + (Lb) = 2Lh + Lb
The surface area refers to the total area of all faces of the prism, including the bases. Since the bases are right triangles, their areas are (1/2)bh, where b and h are the base and height of the right triangle. Therefore, the surface area is:
Surface area = 2(Lh) + (Lb) + 2[(1/2)bh] = 2Lh + Lb + bh
So, without knowing the dimensions of the block, we can still express the lateral area and surface area in terms of the base lengths and height of the right triangle.