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### Unit 8: Lesson 3

Area of composite figures

# Plane figures FAQ

## What is area and why do we need to know it?

Area is the amount of space that a flat shape covers. We can measure area in square units, like square inches, square centimeters, or square tiles. Knowing the area of a shape can help us figure out how much material we need to cover it, how much space we have left, or how to compare different shapes.
For example, if we want to paint a wall, we need to know the area of the wall to buy enough paint. If we want to make a quilt, we need to know the area of each piece of fabric to start with enough of each color. If we want to find out which rug is bigger, we can compare the areas of the rugs.

## How do we find the area of a parallelogram?

A parallelogram is a four-sided shape with opposite sides parallel and equal in length. To find the area of a parallelogram, we need to know the base and the height. The base is any one of the sides, and the height is the perpendicular distance from the base to the opposite side. The area of a parallelogram is the product of the length of the base and the height, or A, equals, b, h.
For example, if a parallelogram has a base of 12, start text, space, c, m, end text and a height of 9, start text, space, c, m, end text, its area is A, equals, 12, times, 9, equals, 108 square centimeters.

## How do we find the area of a triangle?

A triangle is a three-sided shape with three angles. A triangle is also half of a parallelogram.
To find the area of a triangle, we need to know the base and the height. The base is any one of the sides, and the height is the perpendicular distance from the base to the opposite vertex. Since a triangle is half of a parallelogram, the triangle's area is half of the parallelogram's area. The area of a triangle is start fraction, 1, divided by, 2, end fraction the product of the length of the base and the height, or A, equals, start fraction, 1, divided by, 2, end fraction, b, h.
For example, if a triangle has a base of 10, start text, c, m, end text and a height of 8, start text, space, c, m, end text, its area is A, equals, start fraction, 1, divided by, 2, end fraction, times, 10, times, 8, equals, 40 square centimeters.

## How do we find the area of a composite figure?

A composite figure is a shape that is made up of two or more simpler shapes, like rectangles, triangles, circles, or other polygons. To find the area of a composite figure, we can use one of these strategies:
• Split the composite figure into smaller shapes that we know how to find the area of, and then add up the areas of the smaller shapes.
• Subtract the area of the unwanted parts from the area of a larger shape that contains the composite figure.
• Use a formula or a rule that applies to the composite figure, if we know one.
For example, suppose we want to find the area of this composite figure.
A five-sided figure composed of a a rectangle and a triangle. The side lengths measure, in clockwise order, 6 units, 12 units, 15 units, 18 units, and an unlabeled length. The interior angle measures, in clockwise order and starting between the 6 unit and 12 unit sides are 3 right angles, an unlabeled acute angle, and an unlabeled reflex angle.
We can divide it into a rectangle and a triangle, and then add up their areas:
A composite figure consisting of a rectangle and a triangle. The rectangle has a base of 15 units and a height of 12 units. The triangle has a base of 9 units and a height of 6 units.
The area of the rectangle is A, equals, 15, times, 12, equals, 180 square units. The area of the triangle is A, equals, start fraction, 1, divided by, 2, end fraction, times, 9, times, 6, equals, 27 square units. The area of the composite figure is A, equals, 180, plus, 27, equals, 207 square units.