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REVIEW (SPECIAL RIGHT TRIANGLES)
15.
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LESSON
A = base x heightA = bh
Find the perimeter and area of each parallelogram. Round to the nearest hundredths if necessary.EXAMPLES
1) 2) 3) 4)
P = 18 + 18 + 12 + 12P = 60 inches
P = 5 + 5 + 9 + 9 P = 28 feet
P = 3.2 + 3.2 + 3.2 + 3.2or P = (3.2) (4)P = 52.8 meters
P = 13 + 13 + 10 + 10P = 46 yards
A = bh A = bh A = bhA = bh
A = (18 in)(6√3 in)A = 187.06 in2
A = (5 ft)(4.5√3 ft)A = 38.97 ft2
A = (3.2 m)(3.2 m)A = 10.24 m2
A = (13 yd)(5√2 yd)
A = 91.92 yd2
Find the area of the shaded region. Round to the nearest hundredths if necessary.5)
6)
7)
Area of the shaded region = Area of the rectangle 2(Area of the Triangle)
Area of the shaded region = bh 2(½bh)
Area of the shaded region = ((10)(5√2) 2(½(5)(5))
Area of the shaded region = 45.71 mm2
Area of the shaded region = 70.71 25
Area of the shaded region = Area of the big rectangle (Area of the rectangle + Area of the rectangle)
Area of the shaded region = bh (bh + bh)
Area of the shaded region = ((18)(15) ((12)(3) + (4)(8))
Area of the shaded region = 270 (36 + 32)
Area of the shaded region = 270 68
Area of the shaded region =202 cm2
Area of the shaded region = Area of the big rectangle (Area of the rectangle + Area of the square)Area of the shaded region = bh (bh + bh)
Area of the shaded region = ((20)(9.2) (10.8)(6.1) + (3.1)(3.1))Area of the shaded region = 184 (65.88 + 9.61)Area of the shaded region = 184 75.49 Area of the shaded region =108.51 ft2
Find the height and base of each parallelogram given its area. 8) 100 units2 A = bh
100 = (x + 15)(x)100 = x2 + 15x0 = x2 + 15x 1000 = (x + 20)(x 5)x + 20 = 0 x 5 = 0
x = 20 x = 5
base = 20 unitsheight = 5 units
9) 2000 units2A = bh
2000 = (x + 10)(x)2000 = x2 + 10x
0 = x2 + 10x 20000 = (x + 50)(x 40)x + 50 = 0 x 40 = 0
x = 50 x = 40
base = 50 unitsheight = 40 units
LESSON
A = ½ (base)(height)
diagonals
& KITE
EXAMPLESFind the area of each figure. Round to the nearest hundredths if necessary.
1)
A = ½ (8)(14 + 9)
A = ½ (8)(23)
A = (4)(23)A = 92 cm2
2)
ABCD is a rhombusJKLM is a trapezoid
A = ½(48)(40)A = (24)(40)A = 960 m2
3)
ΔFGH + ΔFIHArea of ΔFGH + Area of ΔFIHA = ½ (37)(9) + ½ (37)(18)
A = (18.5)(9) + (18.5)(18)A = 166.5 + 333A = 499.5 in2
FIND MISSING MEASURES4) Rhombus WXYZ has an area of 100 m2. Find WY if XZ = 10 m.
WY and XZ are diagonals
100 = ½ (10)(WY)100 = 5(WY)5 520 = WY
5) Trapezoid PQRS has an area of 250 in2. Find the height of PQRS.
250 = ½(h)(20 + 30)250 = ½(h)(50)250 = 25h25 2510 = h
Find the perimeter and area of each parallelogram. Round to the nearest hundredths if necessary. Show your work.
NAME ________________________PERIOD______
SCORE______DATE______
1) 2) 3)
4)5) 6)
7)8) 9)
Find the area of each figure. Round to the nearest hundredths if necessary. Show your work.11) 12) 13)10)
CLASSWORK on LESSONS 111 to 112
14) 15) 16) 17)
18) 19)Find the missing measure.20) Rhombus RSTU has an area of 675 m2. Find SU.
Find the missing measure for each figure. Show your work.21) Trapezoid ABCD has an area of 750 m2. Find the height of ABCD.
22) Trapezoid GHJK has an area of 188.35 ft2. If HJ = 16.5 ft, find GK.
23) Rhombus MNPQ has an area of 375 in2. If MP = 25 in, find NQ.
24) Rhombus QRST has an area of 137.9 m2. If RT = 12.2 m, find QS.
25) ΔWXY has an area of 248 in2. Find the length of the base.
26) ΔPQS has an area of 300 cm2. Find the height.
Find the area of each figure. Round to the nearest hundredths if necessary. Show your work.
Find the area of each rhombus or kite. Round to the nearest hundredths if necessary. Show your work.27) 28) 29)
30) 31) 32)
33) A = 164 ft2 34) A = 340 cm2 35) A = 247.5 mm2
Find the area of each trapezoid. Round to the nearest hundredths if necessary. Show your work.36) 37) 38)
39) 40)41)
REVIEWTRIGONOMETRIC RATIOS
LESSON
A = ½ (Perimeter)(apothem)
A = ½ Pa
EXAMPLESa) Find the area of a regular pentagon with a perimeter of 40 cm.
b) Find the area of a regular hexagon with a perimeter of 42 yards.
c) Find the area of a regular nonagon with a perimeter of 108 meters.
P = Perimeter of the regular polygona = apothem (a segment that is drawn from the center of a regular polygon I to a side of the polygon)
STEP 1 Find the value of PQ (apothem)
STEP 2 Use the formula A = ½ Pa
STEP 1 Find the value of the apothem
STEP 2 Use the formula A = ½ Pa
STEP 1 Find the value of the apothem
STEP 2 Use the formula A = ½ Pa
b)
EXAMPLESFind the area of each shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.a)
c)
The area of the shaded region is the difference between the area of the circle and the area of the triangle.
Area of the circle Area of the triangleA = πr2 A = ½ bh or A = ½Pa
The area of the shaded region is the difference between the area of the circle and the area of the triangle.
Area of the circle Area of the triangleA = πr2
The area of the shaded region is the difference between the area of the triangle and the area of the circle.
Area of the circleArea of the triangleA = πr2
A = ½ bh or A = ½Pa
A = ½ bh or A = ½Pa
CLASSWORK on LESSON 113NAME_____________________
PERIOD_____
DATE_____
SCORE_____
Find the area of each polygon. Round to the nearest tenth. SHOW YOUR WORK. 1) a regular octagon with a perimeter of 72 inches. 2) a square with a perimeter of 84√2 meters.
3) a square with apothem length of 12 centimeters. 4) a regular hexagon with apothem length of 24 inches.
5) a regular triangle with side length of 15.5 inches. 6) a regular octagon with side length of 10 meters.
Find the area of each shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth. SHOW YOUR WORK.7) 8) 9)
Find the area of each shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth. SHOW YOUR WORK.10) 11) 12)
13) 14) 15)
16) 17) 18) 19)
Find the area of each figure. Round to the nearest tenth if necessary.1)
a)
2)
3) 4)
5) 6)
LESSON
To find the area of an irregular polygon on the coordinate plane, separate the polygon into known figures.
Find the area of each figure. Round to the nearest tenth if necessary.
a)
1) 2)
The vertices of an irregular figure are given. Find the area of each figure. Round to the nearest tenth if necessary.3) M(4, 0), N(0, 3), P(5, 3), Q(5, 0) 4) G(3, 1), H(3, 1), I(2, 4), J(5, 1) K(1, 3)
CLASSWORK on LESSON 114NAME_____________________
PERIOD_____
DATE_____
SCORE_____
Find the area of each figure. Round to the nearest tenth if necessary.1) 2) 3)
4) 5) 6)
7) 8)
Find the area of each figure. Round to the nearest tenth if necessary.9) 10)
The vertices of an irregular figure are given. Find the area of each figure. Round to the nearest tenth if necessary.11) T(4, 2), U(2, 2), V(3, 4), W(3, 2) 12) P(8, 7), Q(3, 7), R(3, 2), S(1, 3), T(11, 1)
LESSONGEOMETRIC PROBABILITY Probability that involves a geometric measure such as length or area.
Find the probability that a point chosen at random lies in the shaded region.a) b)
A SECTOR of a circle is a region of a circle bounded by a central angle and its intercepted arc.
A regular hexagon is inscribed in a circle with a diameter of 14.a) Find the area of the red segment.
b) Find the probability that a point chosen at random lies in the red region.
Find the area of the blue region. Then find the probability that a point chosen at random will be in the blue region.1) 2)
a) Find the area of the blue sector.
b) Find the probability that a point chosen at random lies in the blue region.
CLASSWORK on LESSON 115NAME_____________________
PERIOD_____
DATE_____
SCORE_____
Find the probability that a point chosen at random lies in the shaded region.1) 2)
Find the area of the indicated sector. Then find the probability of spinning the color indicated if the diameter of each spinner is 15 centimeters.3) blue 4) pink 5) purple
Find the area of the indicated sector. Then find the probability of choosing the color indicated if the diameter of each spinner is 15 centimeters.6) red 7) green 8) yellow
9) A skydiver must land on a target of three concentric circles. The diameter of the center circle is 2 yards, and the circles are spaced 1 yard apart. Find the probability that she will land on the shaded area.
Find the area of the shaded region. Then find the probability that a point chosen at random is in the shaded region. Assume all inscribed polygons are regular.10) 11) 12)
A survey was taken at a high school, and the results were put in a circle graph. The students were asked to list their favorite colors. The measurement of each central angle is shown. If a person is chosen at random from the school, find the probability of each response.13) Favorite color is red.
14) Favorite color is blue or green.
15) Favorite color is not red or blue.
16) Favorite color is not orange or green.
