A composite 2D figure is a two dimensional figure made up of basic two dimensional shapes such as triangles, rectangles, circles, semi-circles, etc.

To find the perimeter of a composite 2D figure, add the lengths of the sides.

To find the area of a composite 2D figure, draw any necessary segments to view the figure as basic shapes, then:

• add basic shape areas belonging to the composite shape
• subtract basic shape areas NOT belonging to the composite shape

PROBLEM

Find the perimeter and area of the composite 2D figure below.

View the composite 2D figure as a right triangle together with a rectangle less a semicircle, then find any missing lengths in order to calculate the perimeter and area.

PERIMETER SOLUTION

Since the radius of the semicircle is 20 cm, the distance between the 50 cm and 80 cm side is 40 cm. The hypotenuse of the right triangle can be found by substituting the known lengths of 30 cm and 40 cm into the formula for the Pythagorean theorem. The length of the semicircle (x) can be calculated by multiplying the circumference formula for a circle by one-half.

P: Perimeter of the composite 2D figure.

P = 50 cm + 50 cm + 80 cm + 20π cm;

P = (180 + 20π) cm

Using a calculator, we can estimate this result to two decimal places as 242.83 cm

The perimeter of the given composite 2D figure is (180 + 20π) cm [approximately 242.83 cm].

AREA SOLUTION ONE

A: Area.

A_{composite 2D figure} = A_{right triangle} + A_rectangle - A_semicircle

A_{composite 2D figure} = 600 cm² + 2000 cm² - 200π cm²

A_{composite 2D figure} = 2600 cm² - 200π cm²

A_{composite 2D figure} = (2600 - 200π) cm²

Using a calculator, we can estimate this result to two decimal places as 1971.68 cm²

The area of the given composite 2D figure is (2600 - 200π) cm² [approximately 1971.68 cm²].

AREA SOLUTION TWO

Note that there are other similar ways to calculate the area of the given composite 2D figure. For example rather than viewing the composite 2D figure as a right triangle together with a rectangle less a semicircle, view it as a rectangle less both a right triangle and a semicircle.

A: Area.

A_{composite 2D figure} = A_rectangle - A_{right triangle} - A_semicircle

A_{composite 2D figure} = 3200 cm² - 600 cm² - 200π cm²

A_{composite 2D figure} = 2600 cm² - 200π cm²

A_{composite 2D figure} = (2600 - 200π) cm²

Using a calculator, we can estimate this result to two decimal places as 1971.68 cm²

The area of the given composite 2D figure is (2600 - 200π) cm² [approximately 1971.68 cm²].