Transcript 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 a2:b2.
Side length of Polygon I
a
•
=
Side length of Polygon II b
Perimeter of Polygon I
a
•
=
Perimeter of Polygon II b
Area of Polygon I a2
•
= 2
Area of Polygon II b
Example 1
• The polygons are similar. Find the ratio (shaded to
unshaded) of the perimeters and of the areas. Find the
unknown area.
Example 2
• The polygons are similar. Find the ratio (shaded to
unshaded) of the perimeters and of the areas. Find the
unknown area.
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
Example 4
Use the given area to find XY.
• ABCD ~ WXYZ
Example 5
Use the given area to find XY.
• EFGHJK ~ UVWXYZ
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.
Example 7
• Rhombus RSTU and rhombus VWXY are similar. The area of
RSTU is 384 square feet. The diagonals of VWXY are 24 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 of RSTU.