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Pearson Geometry Common Core, 2011

PG

Pearson Geometry Common Core, 2011 View details

1. Areas of Parallelograms and Triangles

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Exercise 30 Page 620

Divide the polygon into more familiar shapes.

21 units^2

Practice makes perfect

Consider the given figure.

We can divide the given trapezoid into three common polygons. The first is a rectangle with a base of 5 and a height of 3. The second and third are both right triangles consisting of a base of 2 and a height of 3. The triangles are also congruent, as their base and height are the same length.

We will find the area of a rectangle and the area of the triangles one at a time. Then, we will add them to obtain the area of the polygon.

Area of the Rectangle

Recall that the length and with of the rectangle are 3 and 5, respectively. We can substitute this value into the formula for the area of a rectangle.

A=l w

l= 3, w= 5

A=( 3)( 5)

Multiply

A=15

The area of the rectangle is 15 square units.

Area of the Triangle

Note that since the triangles are congruent, their areas are equal. Now recall that the base and the height of each of the triangles are 2 and 3, respectively. We can substitute these values into the formula for the area of a triangle.

A=1/2bh

b= 2, h= 3

A=1/2(2)( 3)

▼

Evaluate right-hand side

Multiply

A=1/2(6)

MoveRightFacToNumOne

1/b* a = a/b

A=6/2

Calculate quotient

A=3

The area of each of the triangles is 3 square units.

Area of the Polygon

We already know the area of the rectangles and the area of each of the triangles.

To find the area of the polygon, we can add these values. Area of the Polygon 15+3+3=21 units ^2

Subchapter links

Lesson Check p.619

Practice and Problem-Solving Exercises p.619-621

Standardized Test Prep p.622

Mixed Review p.622