CPM Homework Help : CCG Problem 5-33

An enclosed figure of a rectangle with a right triangle connected at the top left corner. The top angle of the triangle is 20 degrees. The length of the rectangle is 16 m. The width of the rectangle on the right side is 18 m. The width of the rectangle on the left side with the addition of the triangle is 24 m. Find the area and the perimeter of the figure at right. Be sure to organize your work so you can explain your method later.

Hint:

It will help if you break the shape into smaller, easier shapes.

Draw a line to define the rectangle and the triangle.

More Help 1:

The blue side of the triangle is $24-18=6$ .

More Help 2:

Given the $20^\circ$ angle, and the length of the red side, what trig ratio can you use to determine the length of the blue triangle leg? Once you know the red and blue side, use the Pythagorean Theorem to find the length of the hypotenuse.

Answer:

$\text{Perimeter}\approx78.21$ units (add length of all sides)
$\text{Area}\approx294.55\text{ units}^²$ (find area of triangle and rectangle)