Exercise 9 Page 47

Before we try to find the area of the given figure, notice that the figure can be divided into two trapezoids. Remember to find the lengths of any unknown sides when breaking up the shape!

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In the diagram, we can see that the bases of both trapezoids are 12 meters and 8 meters. We can also see that the height of the top trapezoid is 5 meters. By the Segment Addition Postulate, we know that 5+ h=11. Let's find the height of the bottom trapezoid! 5+ h=11 ⇒ l h=11- 5 h= 6 Now let's see the trapezoids separately with all their dimensions labeled!

To find the area of the top trapezoid, we will substitute b_1= 8, b_2= 12 and h= 5 into the formula for the area of a trapezoid.

A=1/2 h * (b_1+b_2)

SubstituteValues

Substitute values

A=1/2* 5* ( 8+ 12)

AddTerms

Add terms

A=1/2* 5*(20)

Multiply

A=1/2* 100

MoveRightFacToNumOne

1/b* a = a/b

A=100/2

CalcQuot

Calculate quotient

A=50

The area of the top trapezoid is 50 square meters. To find the area of the bottom trapezoid, we will substitute b_1= 8, b_2= 12 and h= 6 into the formula for the area of a trapezoid. Let's do it!

A=1/2 h * (b_1+b_2)

SubstituteValues

Substitute values

A=1/2* 6* ( 8+ 12)

AddTerms

Add terms

A=1/2* 6*(20)

Multiply

A=1/2* 120

MoveRightFacToNumOne

1/b* a = a/b

A=120/2