Perimeter distance polygon sum sides Circumference length circle cm ft Section 1.7 Find Perimeter, Circumference, and Area ______________ is the _____________ around a ____________. It is the _______ of all the ________ of the figure. __________________ is the distance around a ________. Both are measured in units of __________, like _____ or _____. The ________ of polygons and circles is the ____________ covered by the figure. It is measured in ___________ units, like ______ or _____. Perimeter distance polygon sum sides Circumference length circle cm ft area surface squared cm² ft²

Find Perimeter, Circumference, and Area Section 1.7 Find Perimeter, Circumference, and Area Key Concepts: Formulas for Perimeter P, Area A, and Circumference C SQUARE RECTANGLE TRIANGLE CIRCLE length l , width w P = 2l + 2w A = lw side length s P = 4s A = s² side lengths a, b, c, base b, height h P = a + b + c A = ½bh diameter d, radius r C = d or C = 2r A = r² use 3.14 for 

EXAMPLE 1 Find the perimeter and area of a rectangle Find the perimeter and area of the rectangular basketball court shown. Perimeter Area 2l + 2w = P A = lw 2(84) + 2(50) = = 84(50) 268 ft = = 4200 ft²

Find the circumference and area of a circle EXAMPLE 2 You are ordering circular cloth patches for your soccer team’s uniforms. The patch has a diameter of 8 cm. Find the approximate circumference and area of the patch shown.   Area Circumference r = d A =  r ² C = d r = (8)  (3.14)(4)²  8(3.14)  3.14(16) cm²  25.12 cm r = 4 cm  50.24 cm²

GUIDED PRACTICE for Examples 1 and 2 Find the area and perimeter (or circumference) of the figure. If necessary, round to the nearest tenth. 2. P = 2l + 2w = 2(13) + 2(6) = 26 + 12 = 38 m A = l  w = 13(6) = 78 m²  2(2)(3.14)  12.56 C = 2r  12.6 yd  (3.14)(2)²  12.56  12.6 yd² A =  r ²

Standardized Test Practice EXAMPLE 3 Standardized Test Practice Find side lengths QR and RS (Distance Formula) ans QS ( use | x1 – x2| ) QS = 1 – 5 = | –4 | = 4 5 4.1 QR = RS = 4 Perimeter is: P = 4 + 5 + 4.1 = 13.1 units

Solve a multi-step problem EXAMPLE 4 Solve a multi-step problem 60 ft You need to mow the lawn in your backyard. You also need to use the trimmer around the edge. The rectangular lawn is 30 feet by 60 feet. It takes 3 minutes to mow 200 square feet and 2 minutes to edge 30 feet. How many minutes will it take to do both jobs? 30 ft Area Perimeter of lawn. A = lw = 60(30) = 1800 ft² P = 2l + 2w = 2(60) + 2(30) = 180 ft Time to mow Time to trim 1800 ÷ 200 = 9 12 min 9(3 min.) = 27 min 180 ÷30 = 6 6(2 min. ) = 27+ 12 = 39 minutes

GUIDED PRACTICE for Examples 3 and 4 3. Describe how to find the height from F to EG in the triangle. The height is the segment from point F to EG at the point (1,3). The height length is 6.

GUIDED PRACTICE for Examples 3 and 4 Find the perimeter and the area of the triangle shown. 4. EF = (1 – 7) + (6 – 3) 2 = 45 6.7 GF = (1 – 7) + (2 – 3) 2 = 37 6.1 EG = 2 – 6 | –4 | = 4 1 2 A = bh P = EF + GF + EG = 6.7 + 6.1 + 4 = 16.8 un = 1 2 (4) 6 = 12 un²

EXAMPLE 5 Find unknown length The base of a triangle is 28 meters. Its area is 308 square meters. Find the height of the triangle. 1 2 A = bh Area formula = 308 1 2 (28) h Substitute 308 for A and 28 for b. = 308 14h Half of 28. = 22 h Divide by 14. h = 22 m

GUIDED PRACTICE for Example 5 5. The area of a triangle is 64 square meters, and its height is 16 meters. Find the length of its base. 1 2 A = bh = 64 1 2 (16) b = 64 8b = 8 b b = 8 m