Lesson 1.7 Area, Perimeter, and Circumference

Bell Work (Have out 1.6 IP) Suppose that 2 angles are supplementary. The first angle is twice as big as the second. What are the measures of the 2 angles? Ray KM is the angle bisector of ∠JKL. Find the m∠ MKL and m∠ JKL. 3) Name the angle relationship, solve for x, and solve angles a) b)

BellWork 1) The sum of two numbers is 10. Their difference is 2. What are the numbers? 2) Mei and James each improved their yards by planting hostas and geraniums. They bought their supplies from the same store. Mei spent $46 on 4 hostas and 2 geraniums. James spent $39 on 4 hostas and 1 geranium. Find the cost of one hosta and the cost of one geranium. 3) The school is selling tickets to the annual dance competition. On the first day of ticket sales the school sold 15 senior citizen tickets and 16 student tickets for a total of $402. The school took in $314 on the second day by selling 13 senior citizen tickets and 11 student tickets. What is the price each of one senior citizen ticket and one student ticket?

Outcomes You will be able to: Use formulas to calculate perimeter and area for the square, rectangle, and triangle. Use formulas to calculate circumference and area of a circle. Use logic to solve multi-step problems.

Agenda BellWork Notes 1.7 and Whiteboard Practice IP Exit Ticket

Perimeter & Area Square – all four sides are congruent and all four angles are congruent Side length s Perimeter: P = 4s Area: A = s2 s

Perimeter & Area Rectangle– 2 pair of congruent sides, and all four angles are congruent Length l, width w Perimeter: P = 2l + 2w Area: A = l x w

Perimeter & Area Triangle – 3 sided polygon side lengths are a, b, and c ; height h Perimeter: P = a + b + c Area: ½ (bh) c a h b

Example 1. Find the perimeter and area of a square with side length of 12 inches. P = 4 (12) = 48 in A = (12)2 = 144 in2 Don’t forget your units!

Example 2. Find the perimeter and area of a rectangle with a length of 20 inches and a width of 15 inches. Perimeter: P = 2(20) + 2(15) P = 70 inches Area : A = (20)(15) A = 300 in2

White board Practice Find perimeter and area of each figure.

White board Practice

Circumference & Area Circle – All points that are equal distance from a center. Radius r Circumference: C = 2πr = πd Area: A = πr2 Pi is the ratio of a circle’s circumference to its diameter. r

Example 3. Find the area and circumference of a circle with a diameter of 10 centimeters. Use 3.14 as pi. Circumference: C = 2πr = πd C = π(10) = 31.4 cm Area: A = πr2 A = (3.14)(5)2 = 78.5 cm2 10cm

Whiteboard Practice Find circumference/perimeter and area of each figure.

Problem Solving Plan 1. Ask yourself what you need to solve the problem. Write a verbal model or draw a sketch that will help you find what you need to know. 2. Label known and unknown facts on or near your sketch. 3. Use labels and facts to choose related definitions, theorems, or formulas, or other results you may need. 4. Reason logically to link the fats, using a proof or other written argument. 5. Write a conclusion that answers the original problem. Check that your reasoning is correct.

Whiteboard Example

Example The area of a rectangle is 64 m2. The length is four times the width. Find the dimensions of the rectangle. Diagram? What do you know? What do you need? A = l ∙ w = 64 l = 4 ∙ w Width = 4 meters, Length = 16 meters

Example You are putting a fence around a rectangular garden with a length of 15 ft and a width of 8 feet. What is the length of the fence that you will need? Diagram? What size square garden could you make with the same amount of fencing?

Example 3. The Pantheon is a building in Rome which was originally built for the seven Roman deities of the seven planets. The building has a large dome that is 43.3 meters in diameter. What is the circumference of the covered floor? What is the area?

Whiteboard Challenge

Here comes the IP! Here comes the exit ticket!

Exit Ticket