Section 10 4 perimeters areas of similar figures
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Section 10–4 Perimeters & Areas of Similar Figures. Objectives: 1) To find perimeters & areas of similar figures. Reminder of Perimeter & Area. Perimeter – Distance around a figure Perimeter of any polygon - add up the lengths of all of the sides

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Section 10–4 Perimeters & Areas of Similar Figures

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Section 10 4 perimeters areas of similar figures

Section 10–4 Perimeters & Areas of Similar Figures

Objectives:

1) To find perimeters & areas of similar figures.


Reminder of perimeter area

Reminder of Perimeter & Area

  • Perimeter – Distance around a figure

    • Perimeter of any polygon - add up the lengths of all of the sides

    • Perimeter of a circle – Circumference

    • C = 2r

  • Area – How much 2D space it takes up

    • A// = bh

    • AΔ = ½ bh

    • A = r2


Perimeters areas of similar figures

Perimeters & Areas of similar figures

  • If the similarity (side) ratio of 2 similar figures is a/b, then

    • The ratio of their perimeters is a/b.

    • The ratio of their areas is a2/b2.

b

a


Ex 1 find the ratio of the perimeter and the area larger to smaller

Ex.1 Find the ratio of the perimeter and the Area (Larger to smaller)

ΔABC ~ ΔFDE

D

5

Side ratio =

4

6.25

5

B

E

F

7.5

6

Perimeter Ratio = Side Ratio

Perimeter Ratio = 5/4

Area Ratio = a2/b2 =

4

A

C

5

52/42 =

25/16


Ex 2 find the area

Ex.2: Find the area

The ratio of the lengths of the corresponding sides of 2 regular octagons is 8/3. The area of the larger octagon is 320ft2. Find the area of the smaller octagon.

8

Side ratio =

3

Now, set up an area proportion using the area ratio!

82

64

Area ratio =

=

32

9

Large side

Large Area

64

320

=

9

x

x = 45ft2

Small side


Ex 3 find the side ratio

Ex.3: Find the side ratio

The areas of 2 similar pentagons are 32in2 and 72in2. What is their similarity (side) ratio? What is the ratio of their perimeter.

Reduce

Remember: Side ratio is a/b and area ratio is a2/b2. So if the area ratio is given, you must take the square root of the numerator and the denominator.

32

4

2

=

=

3

72

9

Area Ratio

Side Ratio and the Perimeter ratio


Ex 4 find the perimeter area of similar figures

Ex.4: Find the perimeter & area of similar figures.

The similarity (side) ratio of two similar Δis 5:3. The perimeter of the smaller Δ is 36cm, and its area is 18cm2. Find the perimeter & area of the larger Δ.

Write the side ratio and then find the perimeter.

Write the area ratio and then find the area.

52

25

A

5

P

=

=

=

32

9

18

3

36

PL = 60cm

A = 50cm2


What have i learned

What have I Learned??

  • Side Ratio = a/b

  • Perimeter Ratio = a/b

  • Area Ratio = a2/b2

  • If perimeters are given:

    • Write as a ratio

    • Reduce to simplest form for the side ratio

  • If Areas are given:

    • Write as a ratio

    • Reduce until 2 perfect squares are reached.

    • Square Root (√) both numerator & denominator for the side ratio


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