**Perimeter and Area**

**Lesson 8.2**

**In this section,**

Key Concepts:

- To determine the total

of a composite figure, add and/or subtract areas.

To determine the

of a composite figure, add the distances around the outside of the figure.

You will apply

the formulas

for the perimeter

and area of simple

shapes to more

complex shapes.

- A composite figure is made up of

more than one simple shape.

1. Find the area of A1.

2. Find the area of A2.

3. Add the two areas!

perimeter

**of Composite Figures**

This composite figure is

made up of a triangle

and a rectangle

area

e.g.

How can you apply

your knowledge of perimeter

and area to a

composite figure?

Example 1:

Area and Perimeter of a Composite Figure

24cm

12cm

4cm

16cm

a) Determine the area of

the trapezoid shown.

b) Determine the perimeter.

Round to the nearest centimetre.

Solution:

a) The trapezoid can be split into a rectangle and two right triangles.

24cm

12cm

4cm

16cm

Understand the Problem

Choose a Strategy

To find the total area of the trapezoid, add the area of the rectangle and the areas of the two right triangles. Use the formulas for the areas of these shapes.

Area of rectangle: length x width

Area of triangle: base x height / 2

Formulas

Carry Out the Strategy

Call the area of

the rectangle: AR

AR = lw

= (24)(16)

= 384

AT1 = ½ bh

= ½ (12)(16)

= 96

AT2 = ½ bh

= ½ (4)(16)

= 32

Call the area of

the triangle on

the left: AT1

Call the area of

the triangle on

the right: AT2

Call the total area: Atotal

Atotal = AR + AT1 + AT2

= 384 + 96 + 32

= 512

The total area of the

trapezoid is 512cm2.

Conclusion:

b) The perimeter of the

trapezoid includes two unknown side lengths.

When the figure is split into a rectangle

and two right triangles, each unknown side is in a triangle. Apply the Pythagorean theorem to determine the lengths of the two unknown sides in the perimeter.

Understand the Problem

Choose a Strategy

24cm

12cm

4cm

16cm

In both triangles,

the unknown side

is the hypotenuse.

First, find the length of the unknown side on the left.

Call it; c. The length of

c = 20cm.

c² = a² + b²

= 12² + 16²

= 144 + 256

= 400

c = √400

= 20

Next, find the length of the unknown side on the right. Call it d. The length of d = 16cm.

d² = a² + b²

= 4² + 16²

= 16 + 256

= 272

d = √272

= 16

Now, find the perimeter by adding the outside measurements.

P = 24 + 16 + 40 + 20

= 100

The perimeter of

the trapezoid is

approximately 100cm.

Carry Out the Strategy

Conclusion:

Example 2:

Area of a Composite Figure,

by Subtraction, and Perimeter

a) Describe the steps you would use to find the area of the walkway.

b) Calculate the area of the walkway. Round to the nearest tenth of a square metre.

c) The walkway will have a border in a different colour of tile. Calculate the perimeter of the walkway. Round to the nearest tenth of a metre,

A hotel is remodelling its outdoor entrance area.

The new design includes a tile walkway leading to a semicircular fountain.

2.1m

5.2m

Solution:

a) The walkway is a rectangle with a semicircle cut out of it.

Determine the area of the rectangle minus the area of the semicircle.

5.2m

2.1m

b)

AR = lw

= (5.2)(2.1)

= 10.92

Call the area of the rectangle: AR

Call the area of the semicircle: AS

AS = ½ π r ²

= ½ π (1.05) ²

= 1.73

Call the total area of the walkway: AW

AW = AR - AS

= 10.92 - 1.73

= 9.19

The total area of

the walkway is approximately 9.2m²

c) The perimeter of the walkway consists of the three sides of the rectangular section and

the semicircular arc.

First, find the length of the semicircular arc.

L = ½ (πd)

= ½ π(2.1)

= 3.3

Now, add the distances around the outside of the walkway.

Pwalkway = L + 3 sides of rectangle

= 3.3 + (5.2 + 2.1 + 5.2)

= 15.8

Conclusion:

The perimeter of the

walkway is about 15.8m.

Remember these

ANY QUESTIONS?

PRESENTATION BY //

SAMMI CHEN

ANJALI GAUR

GOPPIKKA NATKUNAM