1. Unit 10 Review By Cindy Lee and Nitin Kinra

2. Formulas Heron’s Formula S= a+b+c/2 A= √s(s-a)(s-b)(s-c) Equilateral Triangle A= x² √3/4 Area of Circle A=πr² Area of Sector A= M of arc/360 Ⅹ πr² Probability measure of piece/ measure of whole

3. Concepts of Unit 10 ●All polygon formulas are based on the parallelogram formula (bxh) ●Apothem=distance from the center to side of a polygon If given 1 side to find the area of polygon use ●SohCahToa ●Special right triangle rule

4. Connection ●In Unit 7 we learned the rules for 30 ০ 60 ০ 90 triangles as well as 45 ০ 45 ০ 90 triangles ●In order to find the altitude or height for triangles these rules are a big factor in finding these lengths ●Once you use those rules to find the height you can then find the area of shapes such as triangles which is one of the concepts covered in this unit

5. Examples: Easy: Find the perimeter and area of the following shapes. 1. 2. 5 13 17 10 8 21

6. Explanation: ● In the first example to get the perimeter add all the sides ● In order to get the area use the formula ½(B)(H) ● For the second since it is a right triangle use the pythagorean theorem ● Use same formula for area as the first problem Answer: 1) P: 48 A: 84 2) P: 30 A: 30

7. Examples: Medium: The square has a side length of 10. Find the area of the circles. 10

8. Explanation: ● Since the 2 circles are along a square with a side of 10 the diameter would be 5 ● Therefore the radius is 2.5 ● Use area of circle which is A=πr² ● Since there are 4 circles, multiply the area of circle by 4 Answer: 25π or 78.54

9. Examples: Hard: Find the area of the circle inscribed in a rhombus whose perimeter is 200 and whose longer diagonal is 80. 80

10. Explanation: ● Since the perimeter is 200 and the side length is 50 ● Half of the longer diagonal is 40 ● Use the pythagorean theorem to find the other side length which is 30 ● Use the hypotenuse leg theorem to find the base length of half the triangle ● Create proportions 30/x=50/30 and x=18 ● Then use the special right triangle rule to find the radius of the circle which is 24 ● Then use area of circle formula to find area of the inscribed circle Answer: 576π or 1809.56

11. Common Mistakes In equilateral triangle problems the apothem was occasionally used as the height, and was used in the formula 1/2bh instead of being divided into 3 congruent triangles. Using the correct triangle theorem. To use either 45 ୦ 45 ୦ 90 or 30 ୦ 60 ୦ 90

12. Real Life There is a rectangular garden that is 12 ft wide and 15 ft long. In the middle of the garden there is a sprinkler that sprays water at 7 ft. How much farther does the sprinkler need to spray water to cover the whole garden? 15 12 7

13. Explanation ●First, divide the rectangular garden into 4 rectangles which has the radius (7ft) as the length of the smaller rectangle. ●Next, divide the width of the big rectangle into half which equals 7.5 ft. The 7.5 ft is the width of the smaller rectangle ●Now draw a diagonal in the smaller rectangle. This diagonal will become the radius needed for the sprinkler to cover the garden. ●Using pythagorean theorem the diagonal is 10.26 ft ●Then use the area of the circle formula A=πr² Answer: 105.27π or 330.72