NJ ASK POD In math class, Eddie drew an isosceles, acute triangle. One of the angles has a measure of 42 degrees. What are the other two angle measures of Eddie’s triangle? DO NOW A square and a regular hexagon have the same perimeter. A side of the square is 4.5 inches long. How long is a side of the hexagon?

HW and POW Review – Pg. 538 #1,5,8 Pg. 542 #1,4,7 Pg.548 #1,3,5 Pg.552 #4

Objective TLWBAT create a composite figure of the initials of one’s name by combining different polygons and calculate the area of the figure by applying the appropriate formulas to earn a rubric score of at least 8 out of 10 points. NJCCCS E.1 Common Core 7.G.B.4, 7.G.B.6

Estimating the Area of an Irregular Figure Estimate the area of the figure. Each square represents one square yard. Count the number of filled or almost-filled squares: 45 squares. Count the number of squares that are about half-full: 10 squares. Add the number of filled squares plus ½ the number of half-filled squares: 45 + ( 10) = = The area of the figure is about 50 yd 2.

Check It Out: Example 1 Estimate the area of the figure. Each square represents one square yard. Count the number of filled or almost-filled squares: 11 red squares. Count the number of squares that are about half-full: 8 green squares. Add the number of filled squares plus ½ the number of half-filled squares: 11 + ( 8) = = The area of the figure is about 15 yd. 2

Example 2: Finding the Area of an Irregular Figure Find the area of the irregular figure. Use 3.14 for . Use the formula for the area of a parallelogram. Substitute 16 for b. Substitute 9 for h. A = bh A = 16 9 A = 144Step 1: Separate the figure into smaller, familiar figures. 16 m 9 m 16 m Step 2: Find the area of each smaller figure. Area of the parallelogram:

Example 2 Continued Find the area of the irregular figure. Use 3.14 for . Substitute 3.14 for  and 8 for r. 16 m 9 m 16 m Area of the semicircle: A = (r) ‏ 1 2 __ The area of a semicircle is the area of a circle A ≈ ( ) ‏ 1 2 __ A ≈ (200.96) 1 2 __ Multiply. A ≈

Example 2 Continued Find the area of the irregular figure. Use 3.14 for . A ≈ = The area of the figure is about m 2. Step 3: Add the area to find the total area. 16 m 9 m 16 m

Check It Out: Example 3 Find the area of the irregular figure. Use 3.14 for . Use the formula for the area of a rectangle. Substitute 8 for l. Substitute 9 for w. A = lw A = 8 9 A = 72Step 1: Separate the figure into smaller, familiar figures. 3 yd 9 yd Step 2: Find the area of each smaller figure. Area of the rectangle: 8 yd 9 yd

Check It Out: Example 3 Continued Find the area of the irregular figure. Use 3.14 for . Substitute 2 for b and 9 for h. Area of the triangle: A = bh 1 2 __ The area of a triangle is the b h A = (2 9) ‏ 1 2 __ A = (18) 1 2 __ Multiply. A = 9 2 yd 9 yd 8 yd 9 yd

Check It Out: Example 3 Continued Find the area of the irregular figure. Use 3.14 for . A = = 81The area of the figure is about 81 yd 2.Step 3: Add the area to find the total area.

Problem Solving Application The Wrights want to tile their entry with one- square-foot tiles. How much tile will they need? 5 ft 8 ft 4 ft 7 ft t

Find the area of the floor by separating the figure into familiar figures: a rectangle and a trapezoid. Then add the areas of the rectangle and trapezoid to find the total area. 5 ft 8 ft 4 ft 7 ft t

Find the area of each smaller figure. A = lw A = 8 5 A = 40 Area of the rectangle: Area of the trapezoid: A = 24 A = h(b 1 + b 2 ) ‏ 1 2 __ A = 4(5 + 7) ‏ 1 2 __ A = 4 (12) ‏ 1 2 __ Add the areas to find the total area. A = = 64 The Wrights’ need 64 ft 2 of tile. 5 ft 8 ft 4 ft 7 ft t

Lesson Quiz Find the perimeter and area of each figure cm, cm ft, 84 ft 2

3. Identify the perimeter and area of the figure. A. 50 cm; 42 cm 2 B. 50 cm; 54 cm 2 C. 34 cm; 54 cm 2 D. 34 cm; 42 cm 2 Lesson Quiz

4. Identify the perimeter and area of the figure. A in.; in 2 B in.; in 2 C in.; in 2 D in.; in 2 Lesson Quiz

Closure Find the area by breaking the composite figure into familiar shapes.