Question

Find the volume and surface area of the composite figure shown below if the figure is built with unit cubes.

Answer 1

We can start by breaking down the composite figure into smaller, simpler shapes.

First, let's focus on the rectangular prism at the bottom. It has dimensions of 5 units by 3 units by 1 unit, so its volume is:

5 x 3 x 1 = 15 cubic units

Its surface area can be found by adding up the areas of its six faces. The top and bottom faces are both 5 x 3 = 15 square units, while the four side faces are each 3 x 1 = 3 square units. So the total surface area is:

2(15) + 4(3) = 36 square units

Next, let's consider the triangular prism on top of the rectangular prism. It has a height of 2 units and its base is a right triangle with legs of length 2 and 4 units. So its volume is:

(1/2)x2x4x2 = 8 cubic units

To find its surface area, we need to find the area of each face. The two triangular faces are congruent with area:

(1/2)x2x4 = 4 square units each

And the three rectangular faces have areas of:

2 x 2 = 4 square units

2 x 4 = 8 square units

2 x 2 = 4 square units

So the total surface area of the triangular prism is:

2(4) + 3(4+8) = 36 square units

Finally, we can add the volumes and surface areas of the two shapes to find the total volume and surface area of the composite figure:

Volume: 15 + 8 = 23 cubic units

Surface Area: 36 + 36 = 72 square units