1 / 8

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. Perimeter – Distance around a figure Perimeter of any polygon - add up the lengths of all of the sides

joylyn
Download Presentation

Section 10–4 Perimeters & Areas of Similar Figures

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Section 10–4 Perimeters & Areas of Similar Figures Objectives: 1) To find perimeters & areas of similar figures.

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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

  8. 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

More Related