Question

example
the polygon represents the floor space of a surf shop at the beach. how many square feet of floor space does the surf shop have?
decompose the polygon into two rectangles and a triangle.
area of top rectangle: $bh=(25)(20)=500$
area of bottom rectangle: $bh=(50)(15)=750$
area of triangle: $\frac{1}{2}bh=\frac{1}{2}(25)(20)=250$
total area: $500 + 750+250 = 1,500$
the surf shop has 1,500 ft² of floor space.

1. show another way to find the number of square feet for the surf shop. example.
2. teresa wants to find the area of a wall in her attic. the wall is shaped like the polygons at the right. show two different ways teresa could decompose the wall into triangles, rectangles, or both.

Explanation:

Step1: Decompose the polygon differently

Decompose the polygon into a rectangle and a trapezoid. The rectangle has dimensions 15 ft by 35 ft. The trapezoid has bases 15 ft and 25 ft and height 20 ft.

Step2: Calculate area of rectangle

The area formula for a rectangle is $A = bh$. Here, $b = 35$ ft and $h=15$ ft. So $A_{rectangle}=(35)(15)= 525$ square - feet.

Step3: Calculate area of trapezoid

The area formula for a trapezoid is $A=\frac{(b_1 + b_2)h}{2}$, where $b_1 = 15$ ft, $b_2 = 25$ ft and $h = 20$ ft. So $A_{trapezoid}=\frac{(15 + 25)\times20}{2}=\frac{40\times20}{2}=400$ square - feet.

Step4: Calculate total area

The total area of the polygon is $A = A_{rectangle}+A_{trapezoid}=525 + 400=925$ square - feet.

Answer:

Another way to find the area of the surf - shop floor space is to decompose the polygon into a rectangle and a trapezoid. The area of the rectangle with base 35 ft and height 15 ft is 525 square feet. The area of the trapezoid with bases 15 ft and 25 ft and height 20 ft is 400 square feet. The total area is 925 square feet.