# 10.1 Areas of Quadrilaterals and triangles

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1 10.1 Areas of Quadrilaterals and triangles BASE AND HEIGHT MUST FORM A RIGHT ANGLE!! Draw the diagram, write the formula and SHOW YOUR WORK! FIND THE AREA OF THE FOLLOWING:. A rectangle with one side of length 1 mm and 1. A square with diagonal of length 1 m. The perimeter 40 mm. 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 6. An equilateral with perimeter of 7 cm. 36 perimeter cm. 7. A parallelogram with sides 8 cm and 10 cm and an 8. A trapezoid with bases 13m and 1 m and height 5m. angle of A triangle with sides of lengths 8, 15,

2 All consecutive sides are perpendicular Find each missing measure The area of a triangle is 16 square units. If the height is 18 units, what is the length of the base? 15. 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) 16. The height of a trapezoid is 9 cm. The bases are 8 cm and 1 cm long. Find the area. 17. A trapezoid has an area of cm. If the altitude measure 3 cm and one base measures 36 cm, find the length of the other base. 18. The measure of the consecutive sides of an isosceles trapezoid are in the ratio 8:5::5. The perimeter of the trapezoid is 140 inches. If its height is 8 inches, find the area of the trapezoid A kite has diagonals of 5ft. and 11.3 ft. What is the area of the kite? 3. Find the area of a rhombus whose perimeter is 0 cm and whose diagonal is 8cm. 4. Find the area of a square with a diagonal of length 3.

3 10. Circle and Regular Polygons Regular Polygons: Apothem = Area = 7. Regular hexagon with side 8 cm. 3

4 Find the AREA of the figure. Draw diagram if needed. Show formula that you are using! 1. Square with a diagonal of 14 m.. Rectangle with length of 4 in. and diagonal of 5 in. 3. Parallelogram with sides 10 and 16 and a 30 angle. 4. An equilateral triangle with side of 15 yd. 5. Regular Hexagon with apothem of 3 cm. 6. Rhombus with diagonals of 14 and 1 meters. 7. An isosceles trapezoid with legs of 6 m. and bases of 10 m and 8 m. 8. Circle with circumference of Composite Figures 4

5 10.3 Composite Figures Find the shaded area. Round to the nearest tenth if necessary

6 10.5 SCALE FACTOR = Ratio of corresponding sides in similar polygons Scale Factor= ratio of heights/ ratio of radii/ ratio of bases/ ratio of diameters Are all triangles similar? Are all squares similar? All rectangles? All circles? Scale Factor: Ratio of Perimeters: a b a b a Ratio of Areas: b Ratio of Volume: a 3 b 3 Ex. 1 The ratio of the perimeters of similar triangles is 3: 4. Find the ratio of their areas. Ex. The ratio of the areas of circles is 16 : 49. Find the ratio of their diameters. Ex. 3 The perimeters of similar quadrilaterals are 48 and 60. The area of the smaller quadrilateral is 96 cm. Find the area of the larger quadrilateral. Ex. 4 The areas of similar triangles are 36 and 64. The length of a side of the smaller triangle is 1. Find the length of the corresponding side of the larger triangle. Describe the effect of each change on the area of the given figure. 1. The base of the parallelogram is multiplied by The length of a rectangle with length 1 yd and width 11 yd is divided by The base of a triangle with vertices A(, 3), B(5, ), and C(5, 4) is doubled. 4. The height of a trapezoid with base lengths 4 mm and 7 mm and height 9 mm is multiplied by 1 3. In Exercises 5 8, describe the effect of each change on the perimeter or circumference and the area of the given figure. 5. The length and width of the rectangle are multiplied by The base and height of a triangle with base 1.5 m and height 6 m are both tripled. 6

7 7. The radius of a circle with center (, ) that passes through (0, ) is divided by. 8. The bases and the height of a trapezoid with base lengths 4 in. and 8 in. and height 8 in. are all multiplied by A rhombus has an area of 9 cm. The area is multiplied by 5. Describe the effects on the diagonals of the rhombus. 10. A circle has a circumference of 14 ft. The area is halved. Describe the effects on the circumference of the circle. Find the similarity ratio for each pair of similar figures. 11. Two regular hexagons with areas 8 in. and 3 in. 1. Two squares with areas 81 cm and 5 cm 13. Two s with areas 10 ft and 360 ft 14. Two circles with areas 18π cm and 18 π cm. For each pair of similar figures, the area of the smaller figure is given. Find the area of the larger figure cm 7 in 5 in A = 18in A = 84 cm 1 in 5 in A = 0 in 15 cm 8 in For each pair of similar figures, find the ratio of the perimeters A = 7 cm A = 1 in A = 8 cm A = 1 cm A = 4 in A = 50 cm 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 ft. What is the area of the larger rectangle? 7

8 10.6 Probability is the chance or likelihood that an event will occur. Probability = desired outcome total number of outcomes Ex. 1 There are 30 students in this class and 18 are male. If you choose a student from the class, what is the probability that you will pick a female student. (answer as a % ) Probability with lengths: desired length total length Ex. A point X is picked at random on AF. What is the probability that X is on: A B C D E F a) AC b) CE c) AF desired area Probability with Areas: 40 cm total area Use the square dart board for the following: The radius of the bull s eye is 4 cm. The radius of the middle circle is 8 cm. The radius of the largest circle is 1 cm. ROUND PERCENTS TO NEAREST TENTHS Ex. 3) Suppose you throw a dart onto the square dartboard, find the probability that the dart will land: a) in the bull s eye b) in the shaded area: 8

9 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. 6 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 5 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? Thee 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 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 points 8. 1 point 9. points points points 1. 5 points Find the probability that a point chosen at random from AK is on the given segment. A B C D E F G H I J K CF 5. BI 6. GK 7. FG 8. AK 5 9. AC

10 11. That state of Connecticut is approximated by a rectangle 100 mi by 50 mi. Hartford is approximately at the center of the state. If a meteor hit earth within 00 mi of Hartford, find the probability that the meteor landed in Connecticut. 1. A stop light at an intersection stays red for 60 second, changes to green for 45 seconds, and then yellow for 15 seconds. If Joel arrives at the intersection at a random time, what is the probability that he will have to wait at a red light for more than 15 seconds? Find the area of the following: All consecutive sides are Area= 6 15 scale factor: 3 Circum.= ratio of perimeters: Area: Ratio of areas: 10. Find the base of a rectangle with height 7 cm and area 91 cm. 1. Find the area of a rhombus whose diagonals are 8 cm and 1 cm long. 13. Find the height of a trapezoid with longer base 30 cm, shorter base 1 cm, and area 105 cm. 14. Find the area of a regular hexagon whose radius is 4 in. 15. Find the area of an equilateral whose side is 8 mm. 16. If octagons are similar with a scale factor of 4:7, find the ratio of their areas. 17. Isosceles trapezoid ABCD has bases AB = 37 and CD = 13. If XD = 17, the area of XYCD is what % of the area of ABCD? 18. The area of parallelogram with bases of 6 cm and 1cm and one angle of 30 is? B C 19. The area of a circle is 75. Find the Circumference in terms of. 1. A triangle has a hypotenuse of length 3 cm. What is the area of the triangle? 10 A D

11 . An isosceles right triangle has a hypotenuse with length 10. What is the area of the right triangle? 3. In the diagram, rhombus ABCD has area 16 m and BD = 18m. Find CA. 4. In the diagram, the perimeter of EFGH is 50 mm. If EF = 1 mm, what is the area of the rectangle? 5. A triangle has an area of 50 units. What is the length of the hypotenuse? 6. What is the area of a parallelogram with a 45 degree angle and sides of length 6 cm and 7 cm? E 7. In the diagram, parallelogram TRAC has TR = 1, RA = 14, and RK = 10. What is the area of the parallelogram? H F G 8. A trapezoid has an area of 33 cm. Find the longer base if the shorter base is 4cm and the height is 6 cm. 9. In the diagram, ABCDE is a regular pentagon with side lengths 6m. OX = 4.13 m. Find the area to the nearest tenth of a meter. 10. What is the area of a regular triangle with a radius of 8 units? A B O C R A 13. A regular hexagon has a side of length 8 cm. Find the area of the hexagon. E X 14. Two regular pentagons have sides of 14m and 3.5 m, respectively. Find their scale factor, ratio of their perimeters and areas. 15. Two regular octagons have perimeters 16 cm and 3cm, respectively. Find the scale factor and the ratio of their areas. 16. Two similar polygons have a scale factor 7 : 5. The area of the larger polygon is 147 u. Find the area of the smaller polygon. 17. The areas of circles are 100 and 36. Find the ratio of their radii and their circumferences. 18. The circumference of a circle is 6. Find its area. D T K C 11

12 Chapter 10 Area of D Shapes Tuesday 4/5 Thursday 4/7 Monday 4/11 Wednesday 4/13 Friday 4/15 Tuesday 4/19 Thursday 4/1 Monday 4/ and 10. Areas of Triangles and Quadrilaterals, Circles, and Regular Polygons Packet Pages 1-4 Keys Trip 10.1 and 10. Review Packet Pages 1-4 Keys Trip More Review 10.3 Composite Figures Review Packet Pages 5 QUIZ # Ratios of Similar Figures Packet Pages Geometric Probability Packet Pages 8-10 QUIZ # Review Packet Pages Unit 10 Test HW: HW and Packet Pages 1-4 are due on Wednesday 4/13 Yackey not in class HW and Packet Pages 1-4 are due on Wednesday 4/13 Yackey not in class HW and Packet Pages 1-4 are due on Wednesday 4/13 HW: HW: HW: HW: Finish Packet TURN IN PACKET AT BEGINNING OF CLASS HW: None :) Area of a square: s Perimeter of a square: 4s Area of a Rectangle: bh Perimeter of a Rectangle: b + h or (l + w) bh 1 Area of a Triangle: or bh Area of a Parallelogram: bh d1 d Area of a Rhombus or Kite: b 1 b h Area of a Trapezoid: Area of a Circle: r Area of s Equilateral : or d1 d 1 h b1 b Circumference of a Circle: r or d or measure of arc a Sector : r 360 1

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