10.1 Geometry Areas of Parallelograms, Triangles and Heron s Formula
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1 Name Due Date 4/ Geometry Areas of Parallelograms, Triangles and Heron s Formula Area of a Rectangle: A= Area of a Square: A= Area of a Parallelogram: A= Area of a Triangle: A= Example 1: What is the area of the parallelogram? Note, the CB=8 cm, CD=10 cm and the altitude is 6 cm. Example 2: For ABCD, what is DE to the nearest tenth? 1
2 Example 3: Find the areas of the following figures. If you know the length of the of a triangle, there s a special formula called that allows you to find the without knowing a base and an altitude. Example 4: Find the value of s and calculate the area using Heron s Formula. 2
3 10.2 Geometry Areas of Trapezoids, Rhombuses and Kites Area of a Trapezoid: A= Visualize! How does a trapezoid compare to a parallelogram? How do their area formulas compare? Example 1: What is the approximate area of Nevada? Example 2: Special Right Triangles Review! What is the area of trapezoid PQRS? SR=5 and PQ=7 3
4 Review: Properties of a rhombus: 1. The diagonals are. 2. The diagonals are each other. The diagonals form s. Find the area of the rhomnus with the given information. Area of a Rhombus: A= Draw the longer diagonal in the kite. What do you notice? s. Label and find the area of one. How can you find the area of the kite? Area of a Kite: A= 4
5 Example 3: What is the area of kite KLMN? 5
6 10.3 Geometry Area of Regular Polygons A polygon is a polygon with sides and angles. The of a regular polygon is the distance from the to a. The is the perpendicular distance from the to a. Label the diagram with the new terms. Example 1: Find the measure of the numbered angles, given that the pentagon is a regular pentagon. Example 2: Find the area of the regular pentagon. Hint: First find the area of the triangles, then the area of the polygon. 6
7 Area of a Regular Polygon: Formula for the area of a regular polygon with apothem a and perimeter p is You now have two ways to find the area of a regular polygon. Remember, you must always draw a, drop the to find the of the sides and use special right triangles or to find the. Find the apothem in each of the regular polygons below. Then find the area of each. 7
8 10.4 Geometry Perimeters of Areas of Similar Figures Example 1: Find the scale factor, perimeter and area of the similar figures. Then find the ratio of the perimeters and areas. Example 2: Find the scale factor, ratio of perimeters and ratio of areas of the following similar figures. 8
9 Example 3: The area of the smaller regular pentagon is about 27.5 cm 2. What is the area of the larger regular polygon? Example 4: The rectangles below are similar. What is the ratio of their perimeters? Show all work. 9
10 10.5 Geometry Area of Regular Polygons (Part 2) with Trigonometry Example 2: Find the area of the regular pentagon with 4 inch side lengths. Hint: First draw a picture. Example 3: A table has the shape of a regular octagon with radius of 9.5 in. What is the area of the tabletop to the nearest square inch? 10
11 10.6 Geometry Circles and Arcs Write the definition of the following. Draw and label them on the circle provided. 11
12 Example 2: Give exact answers and approximate answers (nearest 100 th ). Example 4: Find the arc length for the following circles. 12
13 10.7 Geometry Areas of Circles and Sectors Area of a Circle: A= Example 1: Find the area of the following circles. Give both exact answers and approximate answers (nearest 100 th ) a) r = 5 cm b) C = 36π ft Example 2: Determine the radius of the circle with an area of 25π cm 2. Show work 13
14 Area of a Sector: A s = Example 3: Sketch the sector and find the area of the sector with the given information. r = 6, θ = 60 14
15 Example 4: What is the area of the shaded segment? a) b) 15
16 10.8 Geometry Geometric Proability Example 1: Point S on AD is chosen at random. Find the probability that S is on BC. Example 2: Point K on ST is chosen at random. Find the probability that K lies on QR? Example 3: A commuter train runs every 25 minutes. If a commuter arrives at the station at a random time, what is the probability that the commuter will have to wait no more than 5 mins for the train? Hint: draw a line segment to represent the situation. 16
17 The probability that a point S lies in part of a region can be represented with the equation: P(S in desired region) = of desired region of total (entire)region Example 4: A triangle is inscribed in a square. Point T in the square is selected at random. What is the probability that T lies in the shaded region? Example 5: Suppose you have a simple dart board as shown. The small circle has a radius of 3 in. and each section also has a width of 3 in. Assuming the dart lands on the board, find the probability that at dart lands in the outer ring, the middle ring and the inner circle. P(outer ring) = P(middle ring) = P(inner circle) = What do you notice about the sum of the probabilities? Why do you think that is? 17
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