Introduction to Perimeter, Circumference and Area Geometry Introduction to Perimeter, Circumference and Area

Geometry 1.7 Perimeter, Circumference, Area Goals: Find the perimeter and area of common plane figures. Use a general problem-solving plan. September 11, 2018 Geometry 1.7 Perimeter, Circumference, Area

Geometry 1.7 Perimeter, Circumference, Area Square Perimeter P = 4s S S Area A = s2 September 11, 2018 Geometry 1.7 Perimeter, Circumference, Area

Geometry 1.7 Perimeter, Circumference, Area Square Problem Each side of a square measures 2.5 m. Find its perimeter and its area. P = 4(2.5) = 10 m A = 2.52 = 6.25 m2 2.5 m 2.5 m Area is a square measure. September 11, 2018 Geometry 1.7 Perimeter, Circumference, Area

Geometry 1.7 Perimeter, Circumference, Area Rectangle Perimeter P = 2 l + 2w w Area A = lw l September 11, 2018 Geometry 1.7 Perimeter, Circumference, Area

Geometry 1.7 Perimeter, Circumference, Area Rectangle Problem Find the perimeter and the area. 4 ft 2.1 ft P = 2(4) + 2(2.1) = 8 + 4.2 = 12.2 ft A = 4(2.1) = 8.4 ft2 September 11, 2018 Geometry 1.7 Perimeter, Circumference, Area

Geometry 1.7 Perimeter, Circumference, Area Triangle Perimeter P = a + b + c c a h Area b September 11, 2018 Geometry 1.7 Perimeter, Circumference, Area

Geometry 1.7 Perimeter, Circumference, Area Triangle Problem Find the perimeter and the area. 8 in 3 in 2 in 10 in P = 3 + 10 + 8 = 21 in A = ½ (10)(2) = 10 in2 September 11, 2018 Geometry 1.7 Perimeter, Circumference, Area

Geometry 1.7 Perimeter, Circumference, Area Circle Circumference C = 2r r Area A = r2 September 11, 2018 Geometry 1.7 Perimeter, Circumference, Area

Geometry 1.7 Perimeter, Circumference, Area Circle Problem If the diameter is 8, find the circumference and the area. r = 4 8 C = 2(4) = 8  25.13 (You could also use the formula C = d.) A = (42) = 16  50.27 September 11, 2018 Geometry 1.7 Perimeter, Circumference, Area

Area of a Trapezoid b1 h b2 September 11, 2018

Area of a Rhombus d1 d2 September 11, 2018

Area of a Kite d2 d1 September 11, 2018

Geometry 1.7 Perimeter, Circumference, Area Problem Solving Ask: What do I need to solve this problem? Draw a picture, if necessary, to help you determine this. Label known and unknown facts. Use labels and facts to choose related definitions, theorems, formulas, or other results you may need. Reason logically to link the facts. Use a proof or other written argument. Write a conclusion that answers the original problem. Check that your reasoning is correct. September 11, 2018 Geometry 1.7 Perimeter, Circumference, Area

Geometry 1.7 Perimeter, Circumference, Area Problem Solving Steps Sketch Label Formulas Reason Conclusion Check September 11, 2018 Geometry 1.7 Perimeter, Circumference, Area

Geometry 1.7 Perimeter, Circumference, Area Problem 1 A homeowner needs to fertilize a rectangular shaped yard that measures 20 ft by 30 ft. Each bag of fertilizer covers 150 square feet. How many bags of fertilizer will he need? 1. Sketch 2. label 30 ft. A = ? 20 ft September 11, 2018 Geometry 1.7 Perimeter, Circumference, Area

Geometry 1.7 Perimeter, Circumference, Area Problem 1 Continued A homeowner needs to fertilize a rectangular shaped yard that measures 20 ft by 30 ft. Each bag of fertilizer covers 150 square feet. How many bags of fertilizer will he need? 3. Formula: A = LW a = 30(20) = 600 FT2 30 ft. A = ? 20 ft September 11, 2018 Geometry 1.7 Perimeter, Circumference, Area

Geometry 1.7 Perimeter, Circumference, Area Problem 1 Continued A homeowner needs to fertilize a rectangular shaped yard that measures 20 ft by 30 ft. Each bag of fertilizer covers 150 square feet. How many bags of fertilizer will he need? 4. Reason: Each bag covers 150 sq ft, and he needs to cover 600 sq ft. 600  150 = 4 30 ft. 20 ft A = 600 FT2 September 11, 2018 Geometry 1.7 Perimeter, Circumference, Area

Problem 1 Conclusion A homeowner needs to fertilize a rectangular shaped yard that measures 20 ft by 30 ft. Each bag of fertilizer covers 150 square feet. How many bags of fertilizer will he need? 5. Conclusion: He needs to buy 4 bags of fertilizer. 30 ft. 6. Check: 4  150 = 600 20 ft A = 600 FT2 September 11, 2018 Geometry 1.7 Perimeter, Circumference, Area

Geometry 1.7 Perimeter, Circumference, Area Problem 2 You are making a mat for a picture. The picture is 8 inches wide and 10 inches high. The mat is to have a width of 2 inches. What is the area of the mat? 8 2 10 2 September 11, 2018 Geometry 1.7 Perimeter, Circumference, Area

Geometry 1.7 Perimeter, Circumference, Area Problem 2 Continued You are making a mat for a picture. The picture is 8 inches wide and 10 inches high. The mat is to have a width of 2 inches. What is the area of the mat? Think: Larger mat, cut away the inside… September 11, 2018 Geometry 1.7 Perimeter, Circumference, Area

Geometry 1.7 Perimeter, Circumference, Area Problem 2 Continued You are making a mat for a picture. The picture is 8 inches wide and 10 inches high. The mat is to have a width of 2 inches. What is the area of the mat? We need to know the area of the outer rectangle. 12 Left over Area = 168 – 80 = 88 in2 Outer Area = 12  14 = 168 8 14 2 10 Inner Area = 8  10 = 80 2 September 11, 2018 Geometry 1.7 Perimeter, Circumference, Area

Geometry 1.7 Perimeter, Circumference, Area Problem 3: You do it. You are making a triangular shaped window. The height of the window is 18 inches and the area will be 297 square inches. What will the length of the base of the window be? 18 b The base will be 33 in. September 11, 2018 Geometry 1.7 Perimeter, Circumference, Area

Geometry 1.7 Perimeter, Circumference, Area Homework September 11, 2018 Geometry 1.7 Perimeter, Circumference, Area