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Notes 73: (11.3) Perimeter and Area of Similar Figures

Notes 73: (11.3) Perimeter and Area of Similar Figures. THEOREM 11.7: AREAS OF SIMILAR POLYGONS. If two polygons are similar with the lengths of corresponding sides in the ratio of a:b, then the ratio of their areas is a 2 :b 2 . = = = . Example 1.

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Notes 73: (11.3) Perimeter and Area of Similar Figures

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  1. Notes 73: (11.3) Perimeter and Area of Similar Figures

  2. THEOREM 11.7: AREAS OF SIMILAR POLYGONS • If two polygons are similar with the lengths of corresponding sides in the ratio of a:b, then the ratio of their areas is a2:b2. • = • = • =

  3. Example 1 • The polygons are similar. Find the ratio (shaded to unshaded) of the perimeters and of the areas. Find the unknown area.

  4. Example 2 • The polygons are similar. Find the ratio (shaded to unshaded) of the perimeters and of the areas. Find the unknown area.

  5. Example 3 The ratio of the areas of two similar figures is given. Write the ratio of the lengths of corresponding sides. • Ratio of areas = 169:144 • Ratio of areas = 125:108

  6. Example 4 Use the given area to find XY. • ABCD ~ WXYZ

  7. Example 5 Use the given area to find XY. • EFGHJK ~ UVWXYZ

  8. Example 6 • ABC and DEF are similar. The height of ABC is 30 inches. The base of DEF is 8 inches and the area is 40 square inches. Find the area of ABC.

  9. Example 7 • Rhombus RSTU and rhombus VWXY are similar. The area of RSTU is 384 square feet. The diagonals of VWXY are24 feet long and 18 feet long. Find the area of VWXY. Then use the ratio of the areas to find the lengths of the diagonals of RSTU. Find the length of a side ofRSTU.

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