Geometry Notes G.14 (11.1 11.2 11.3) Area of Polygons / Similar Figure Ratios
Mrs. Grieser
Name: _______________________________ Date: _____________ Block: _______
Area of Triangles, Parallelograms, Trapezoids, Rhombuses, Kites
Area Formulas:
Rectangle: A = bh
Parallelogram: A = bh
1
bh
2
1
Trapezoid: A = h(b1 + b2)
2
1
Rhombus / Kite: A = d1d2
2
Triangle: A =
Area of a Regular Polygon: A =
Examples:
1
ap, where a = apothem, p = perimeter
2
a) Find the area of the
parallelogram:
b) Find the area of the triangle:
c) The area of a triangle is 50
in2. Its base is 4 times its
height. Find the base and
height.
d) Find the area of the rhombus:
e) Find the area of the kite:
f) Find the measure of the bases
in the trapezoid
if its area is
95 m2:
You try:
a) Find the area of the
parallelogram:
b) Find x in the parallelogram
if A =
70 ft2.
c) Find the area of the rhombus:
d) Find x in the
kite given its
area is 72.25 m2:
e) One diagonal of a kite is
three times as long as the
other diagonal. The area of
the kite is 384 in2. What are
the lengths of the diagonals?
f) Find the area
of the regular
pentagon
shown.
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Geometry Notes G.14 (11.1 11.2 11.3) Area of Polygons / Similar Figure Ratios
Mrs. Grieser
Perimeter and Area of Similar Figures
We have seen in similar figures: ratio of side lengths = ratio of perimeters
Area of Similar Polygons Theorem
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
side length of Polygon II
a
;
b
area of Polygon I
area of Polygon II
a2
b2
Examples:
a) The perimeter of ∆ABC is 24 feet and its area is 24 ft2. The perimeter of ∆JKL is 36 feet.
Given ∆ABC ~ ∆JKL, find the ratio of the area of ∆ABC to the area of ∆JKL. Then find the
area of ∆JKL.
Ratio of perimeters: _______ Ratio of areas: _________ Area ∆JKL: ________
b) The ratio of the areas of two regular decagons is 20:36. What is the ratio of their side
lengths in simplest radical form?
c) Given the figures are similar, find the area
of the smaller figure.
d) Given the figures are similar, find AB.
You Try:
a) Given the two figures are similar, find the ratio
of the perimeters and areas of ∆ABC to ∆DEF. If
the area of ∆ABC is 24,
what is the area of
∆DEF?
b) A large rectangular baking pan is 15 inches
long and 10 inches wide. A smaller pan is
similar to the large pan. The area of the
small pan is 96 in2. Find the width of the
smaller pan.
c) A large rectangular billboard is 12 ft high
and 27 ft long. A smaller billboard is similar
to the larger billboard and has area 144 ft2.
Find the height of the smaller billboard.
d) Rectangle I and II are similar. The
perimeter of Rectangle I is 48 inches.
Rectangle II is 30 inches by 18 inches. Find
the area of Rectangle I.
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