Composite Composite FiguresFigures

All in OneAll in One

Composite figuresComposite figuresComposite figures are two or more Composite figures are two or more

basic figures that can be combined.basic figures that can be combined.

5 cm

7 cm

Find the perimeter of this figure, which consists of a semicircle and a rectangle.7 cm

5 cmP=l+l+w+πd/2

P=(5)+(5)+(7)+π(7)/2

P=17+21.99/2

P=17+10.99 or 11

P=28cm2

Composite figureComposite figuress

Now we need to find the perimeter of Now we need to find the perimeter of three sides of the rectangle at the three sides of the rectangle at the bottom of the figure.bottom of the figure.

Total Perimeter = Circumference of top + Perimeter of bottom

= 11 cm + 17 cm

= 28 cm

ProblemProblemSolutionSolution--we want to find the perimeter of the building. So we we want to find the perimeter of the building. So we

break the composite figure into three basic shapesbreak the composite figure into three basic shapes--two two rectangles and one square. rectangles and one square.

170170

40 40

115115

210 210

115 170 115

170We find the lengthOf the indented part of Each rectangular shapeBy subtracting 170 cmFrom 210 cm to get 40 cm.

P = (115 + 210 + 115 + 40) + (170 + 170)+ (115 + 210 + 115 + 40)

P = 1,300 cm

What is the perimeter of What is the perimeter of the composite figure?the composite figure?

5 5 cmcm 3 3 cmcm

4 4 cmcm

4 4 cmcm 3 3 cmcm 5 5 cmcm

Find the lengths of the missing sides. Then add the side Find the lengths of the missing sides. Then add the side lengths.lengths.

Use the properties of congruent figures to find the missing Use the properties of congruent figures to find the missing measures.measures. The rectangle has a width of 4 The rectangle has a width of 4 cmcm.. The left side of the rectangle is 4 The left side of the rectangle is 4 cm.cm.

Add the lengths of the sides.Add the lengths of the sides. 5 5 cmcm + 3 + 3 cmcm + 4 + 4 cmcm + 4 + 4 cmcm + 5 + 5 cmcm + 3 + 3 cmcm + 4 + 4 cmcm + 4 + 4 cmcm = 32 = 32

cmcm The perimeter of the figure is 32 The perimeter of the figure is 32 cmcm..

4 cm

Hint: Hint: To determine the perimeter of a composite figure, To determine the perimeter of a composite figure, measure the distance around the outside of the figure.measure the distance around the outside of the figure.

4 4 cmcm

Bill is painting his basement floor.

The dimensions are:

3.2 m

1.8 m

2.3 m

2.5 mIf one can of paint will cover 3.5 m2, and each can of paint costs $15.25, what is his total cost?

a) Determine the total area.

A = 2.3 x 2.5 + 3.1 x 1.5

A = 5.75 + 4.65

A = 10.4 m2

Atotal = A1 + A2

3.2 m

1.8 m

2.3 m

2.5 m

A2

A1

b) If one can of paint covers 3.5 m2, how many cans of paint will he need?

2

2

10.4 mNumber of cans

3.5 m /can

Number of cans 2.97

He will need about three cans of paint.

3.2 m

1.8 m

2.3 m

2.5 m10.4 m2