Area and Volume

The area of a figure is the number of square units it takes to completely fill a space or surface.   Area is measured in square units.   Recall that the area of a parallelogram is base x height.

If you divide a parallelogram into two congruent triangles, the area of each triangle is ½ x base x height.

A trapezoid can be divided into a rectangle and two triangles.   The area of a trapezoid is the sum of the areas of the rectangle and the triangles.

You can find the area of irregular polygons by decomposing the polygon into rectangles, triangles and other shapes.

Volume  is the number of cubic units needed to fill a space.   Volume is measured in cubic units.   The volume of a prism is found by multiplying the area of the base times the height.

The surface area of a three-dimensional figure is the sum of the areas of its surfaces.

(source)

Practice

1)  A triangular prism has a triangular end with a base of 4 inches and a height of 3 inches. The length of each side is 5 inches and the width of each side is 3 inches. What is the surface area and volume of the prism?

2)  A triangular prism has a triangular end with a base of 4 feet and a height of 5 feet. The length of each side is 6 feet and the width of each side is 5 feet. What is the surface area and volume of the prism?

3)  Find the surface area and volume of a rectangular prism with a length of 10 m, a width of 8 m and a height of 2 m.

4)  Find the surface area and volume of a rectangular prism with a length of 6 m, a width of 5 m and a height of 3 m.

5)  What’s the area of a trapezoid with 5 units and 8 units as its bases with a height of 10 units?

6)  What’s the perimeter of a hexagon with a side length of 7 cm?

 

(questions adapted from source)