Exercise 12 Page 334

Before we try to find the area of the given figure, notice that the figure can be divided into a rectangle and a triangle.

In the diagram, we can see that the length and width of the rectangle are 15 yards and 12 yards, respectively. We can also see that 15 yards is the base of the triangle and 3 yards is the height. Let's see the figures separately with all their dimensions labeled!

To find the area of the rectangle, we will substitute l= 15 and w= 12 into the formula for the area of a rectangle.

A=l w

SubstituteII

l= 15, w= 12

A= 15( 12)

Multiply

Multiply

A=180

The area of the rectangle is 180 square yards. To find the area of the triangle, we will substitute b= 15 and h= 3 into the formula for the area of a triangle, and simplify.

A=1/2bh

SubstituteII

b= 15, h= 3

A=1/2( 15)( 3)

Multiply

Multiply

A=1/2(45)

MoveRightFacToNumOne

1/b* a = a/b

A=45/2

CalcQuot

Calculate quotient

A=22.5

The area of the triangle is 22.5 square yards. We now know the areas of both the rectangle and the triangle.

To find the total area of the figure, we add these two values. Area of the Figure 180+22.5=202.5yd^2 The total area of the figure is 202.5 square yards.