10.1 Areas of Quadrilaterals and triangles
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Draw the diagram, write the formula and SHOW YOUR WORK! FIND THE AREA OF THE FOLLOWING:
1. A square with diagonal of length 12 m.
2. A rectangle with one side of length 12 mm and the perimeter 40mm.
3. A parallelogram with base 7 m and height 3 m.
4. A rectangle with diagonal of length 17 cm and base length of 15 cm.
5. An isosceles  with base length 10 cm and 36cm perimeter
6. An equilateral  with perimeter of 27 cm.
7. A parallelogram with sides 8 cm and 10 cm and an angle of 60.
8. A trapezoid with bases 13m and 21 m and height 5m.
9. A triangle with sides of lengths 8, 15, 17.
10. A rhombus whose perimeter is 20 cm and whose diagonal is8 cm.
Find each missing measure.
11. The area of a triangle is 216 square units. If the height is 18 units, what is the length of the base?
12. The area of a trapezoid is 80 square units. If its height is 8 units, find the length of its median. (median = average of the bases)
13. The height of a trapezoid is 9 cm. The bases are 8 cm and 12 cm long. Find the area.
14. A trapezoid has an area of 908.5 cm2. If the altitude measure 23 cm and one base measures 36 cm, find the length of the other
base.
15. The measure of the consecutive sides of an isosceles trapezoid are in the ratio 8:5:2:5. The perimeter of the trapezoid is 140
inches. If its height is 28 inches, find the area of the trapezoid.
16. A kite has diagonals of 5ft. and 11.3 ft. What is the area of the kite?
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10.2 Circle and Regular Polygons
Area of Regular Polygons
Center of a Regular Polygon: The center of the circumscribed circle.
Radius of a Regular Polygon: The distance from the center to a vertex.
Central Angle of a Regular Polygon: An angle formed by two radii drawn to consecutive vertices. Find using 360 divided
by the number of sides the polygon has.
Apothem of a Regular Polygon: The (perpendicular) distance from the center of the polygon to a side.
Example: Identify the following on the given regular hexagon.
Center:
D
E
Radius:
Central Angle:
O
Measure of the Central Angle:
C
F
Apothem:
A
X
B
Use the following formula to find the area of a Regular Polygon.
Example 1: Find the area of an equilateral
triangle with an apothem of 3 cm.
Example 2: Find the area of a
regular hexagon with a radius of 7m.
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Example3; Find the area of a regular
pentagon with side length of 5 ft.
Find the area of the following:
Regular hexagon with side 8 cm.

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10.3 Composite Figures
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Find the shaded area. Round to the nearest tenth if necessary.
1.
2.
3.
4.
5.
6.
7.
8.
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10.5 RATIO OF SIMILAR FIGURES:
SCALE FACTOR = Ratio of 2 corresponding sides in 2 similar polygons
Scale Factor= ratio of 2 heights/ ratio of 2 radii/ ratio of 2 bases/ ratio of 2 diameters …
All circles are similar! Are all triangles similar?________Are all squares similar?______ All rectangles? _____
Scale Factor:
a
b
Ratio of Perimeters:
a
b
a2
b2
Ratio of Areas:
a3
b3
Ratio of volumes:
Ex. 1 The ratio of the perimeters of 2 similar triangles is 3: 4.
Find the ratio of their areas. _____________
Ex. 2 The ratio of the areas of 2 circles is 16 : 49.
Find the ratio of their diameters. ______________
Ex. 3 The perimeters of 2 similar quadrilaterals are 48 and 60. The area of the smaller quadrilateral is 96 cm2. Find the
area of the larger quadrilateral.
Ex. 4 The areas of 2 similar triangles are 36 and 64. The length of a side of the smaller triangle is 12. Find the length of
the corresponding side of the larger triangle.
Find the similarity ratio for each pair of similar figures.5
11. Two regular hexagons with areas 8 in.2 and 32 in.2
12. Two squares with areas 81 cm2 and 25 cm2
2
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13. Two ∆’s with areas 10 ft and 360 ft
14. Two circles with areas 128π cm2 and 18 π cm2.
For each pair of similar figures, the area of the smaller figure is given. Find the area of the larger figure.
15.
16.
19.
7 cm
7 in
5 in A = 18in2
A = 84 cm 2
15 cm
5 in
12 in
8 in
A = 20 in 2
For each pair of similar figures, find the ratio of the perimeters.
17.
A = 27 cm 2
18.
22.
A = 1 in 2
A = 12 cm 2
A = 4 in 2
A = 8 cm 2
A = 50 cm 2
19. The shorter sides of a rectangle are 6 ft. The shorter sides of a similar rectangle are 9 ft. The area of the smaller rectangle is 48
ft2. What is the area of the larger rectangle?
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10.6 Probability = wanted outcome / total possible outcomes
(Shaded Area / Total Area)
Find the probability that a point, chosen at random, belongs to the shaded sub regions of the following regions.
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1.
2.
3
4
3.
6
3
6
4
4
4
4
4
5
6
5
6
4.
4
6
5.
6.
5
4
6
5
6
6
6
6
5
5
5
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The dart board shown has 5 concentric circles whose centers are also the center of the square board.
Each side of the board is 38 cm, and the radii of the circles are 2 cm, 5 cm, 8 cm, 11 cm, and 14 cm.
A dart hitting within one of the circular regions scores the number of points indicated on the board, while a hit anywhere else scores
0 points.
If a dart, thrown at random, hits the board, find the probability of scoring the indicated number of points.
7. 0 points
8. 1 point
9. 2 points
10. 3 points
11. 4 points
12. 5 points
̅̅̅̅ .
13. A point X is picked at random on 𝐴𝐹
What is the probability that X is on:
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a) ̅̅̅̅
𝐴𝐶
b) ̅̅̅̅
𝐶𝐸
c) ̅̅̅̅
𝐴𝐹
4
3
2
0
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Ex 4. Find the probability that if a point is chosen inside the square,
it will lie outside the circle.
Ex. 5 Find the probability that if a point is
inside the hexagon, it will lie in the
shaded region.
11 in.
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
Ex. 6 Find the probability that if a tack is dropped in the rectangle, it will land
a) in the circle
b) outside of
the circle
Ex. 7 To win a carnival game, Max must throw a dart at a board four feet by three
feet and hit one of the 25 circles on the board. The diameter of each circle is 4
inches. Approximately what percent of the time will a randomly thrown dart that
hits the board also hit a circle?
Ex. 8 A rectangle contains two inscribed semicircles and a full circle, as shown below. If a point is chosen at random
inside the rectangle, what is the approximate probability that the point will also be in the shaded region?
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