Question

In the figure below, the two triangular faces of the prism are fight triangles with sides of length 3, 4, and 5. The other three faces are rectangles. What is the surface area of the prism. 84 sq. units 96 sq. units 108 sq. units 72 sq. units

can someone please explain how to get the awnser...

Answer 1

The figure of the prism is attached below.

The total surface area of the prism equals the sum of areas of two triangles and the three rectangles.

Surface Area of Prism = Area of 2 Triangles + Area of 3 Rectangles.

Area of a Triangle = 0.5 x Base x Height
Area of a Triangle = 0.5 x 3 x 4 = 6 square units

There are 3 rectangles. From the figure we can see that the bottom most rectangle has the dimensions 4 by 6. The left most rectangle has the dimensions 3 x 6 and the right most rectangle has the dimensions 5 by 6.

So, the Area of 3 rectangles will be = (4 x 6) + (3 x 6) + (5 x 6) = 72 square units

The Surface Area of the prism will be:

Surface Area = 2 (4) + 72 = 84 square units

Thus the correct answer is option A