13 PERIMETER AND AREA OF 2D SHAPES
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1 13 PERIMETER AND AREA OF D SHAPES 13.1 You can find te perimeter of sapes Key Points Te perimeter of a two-dimensional (D) sape is te total distance around te edge of te sape. l To work out te perimeter of a rectangle you can use te following formula. Perimeter of a rectangle l w l w l w w l te lengt of te rectangle w te widt of te rectangle Example 1 Work out te perimeter of te following sape. 9 cm Exam Tip Make sure tat you know te lengts of all te sides efore you work out te perimeter. Missing lengt 8 3 First, fi nd te missing lengt. Perimeter Ten, add te lengts of all six sides. Example Te diagram sows a field in te sape of a trapezium. Te farmer wants to put fencing all te way round te edge of te field. Fencing costs 6.50 per metre. Te farmer as a udget of 000. Can e afford to uy te fencing? 80 m 50 m 110 m 100 m Perimeter m Total cost Te farmer cannot afford to uy te fencing as it costs 10 and e as only 000. First, work out te perimeter. Use te perimeter to fi nd te total cost. Make your fi nal decision clear. 140
2 13 PERIMETER AND AREA OF D SHAPES Exercise 13A 1 Work out te perimeters of te following sapes. a c Questions in tis capter are targeted at te grades indicated. F 4. m 5.7 m cm cm 3.8 m Eac side of a regular pentagon as lengt. Work out te perimeter of te pentagon. 3 Work out te perimeter of tis trapezium. E 4 Te perimeter of an equilateral triangle is 1.. Work out te lengt of eac side. 1 cm 5 Te diagram sows Mrs Smit's lawn. Se wants to put edging all te way round te edge of er lawn. Edging costs 3.80 per metre. Mrs Smit as a udget of 100. Can se afford te edging? Explain your answer. 8 m D 4 m 141
3 13. You can rememer and use formulae to find te area of triangles and quadrilaterals Key Points Area of a rectangle lengt widt l w l w Area of a triangle 1_ ase vertical eigt 1_ Area of a parallelogram ase vertical eigt Area of a square lengt lengt l l l l l Area of a trapezium 1_ sum of te lengts of te parallel sides distance etween te parallel sides 1_ (a ) a 1 (a ) Example 3 Work out te area of tis triangle. Area of triangle 1 ase vertical eigt cm Coose te formula to use. Put in te values of and. Exam Tip Always rememer to include te units in your answer. 14
4 Example 4 Work out te area of tis trapezium. 13 PERIMETER AND AREA OF D SHAPES Area of trapezium 1 sum of parallel sides distance etween parallel sides 7 cm 1 (a ) 1 (5 7) 4 Coose te formula to use. Put in te values of a, and Exercise 13B 4.5 m 3.1 m 1 A decorator wants to paint two rectangular walls. Te walls are 4.5 m y. and 3.1 m y.. Wat is te total area of te two walls to e painted?. E Find te area of te following triangles. a c D 4. 9 cm 3 A company makes flags in tis sape. It makes 50 identical flags. Work out te area of faric used to make tese flags. 1 4 A tiler creates te following pattern using parallelogram-saped tiles. Work out te total area covered y te red tiles. 40 cm 5 Work out te area of eac trapezium. a cm 1 cm 9 cm 00 cm C 6 A trapezium as an area of 40 cm. Te two parallel sides ave lengts 7 cm and 1. Te distance etween te two parallel sides is cm. Work out te value of. 1 7 cm 143
5 13.3 You can find te areas of more complicated sapes Key Point To find te area of more complicated sapes you will need to split te sape into a numer of simpler sapes suc as rectangles, squares, triangles or parallelograms. You can ten find te area of eac part and add tese areas togeter to find te total area. Example 5 Find te area of tis sape. A B Split te sape into two rectangles, A and B Area of rectangle A cm Area of rectangle B cm Total area 1 50 Work out te area of rectangle A. Work out te area of rectangle B. Add te two areas to fi nd te total area of te sape. Exam Tip Rememer to sow ow you split up te sape. You migt get marks for tis in te exam. Example 6 Te diagram sows te plan of a garden. Mr Jones wants to spread grass seed over te garden. One ox of grass seed is enoug for 10 m. How many oxes of grass seed will e need m 11 m m Area of sape area of triangle area of square Split into simpler sapes. 4 m 5 m 11 m Area of square l 6 3 Calculate te area of te square. 144
6 13 PERIMETER AND AREA OF D SHAPES Area of triangle m Total area Amount of grass seed oxes Work out any unknown lengts you need and mark tem on te diagram. Ten calculate te area of te triangle. Add te two areas to fi nd te total area of te sape. Te numer as got to e te next wole numer iger tan te answer, not just rounded to te nearest wole numer. Exercise 13C 1 Te floor of te all in a ouse is a y 150 cm rectangle. Tiles wic are squares of side 1 are used to tile te floor. Work out ow many tiles are needed. Liam wants to replace te carpet in is room. Te floor of te room is a rectangle measuring 4 metres y etres. Te carpet e wants to uy costs 8.65 per square metre. Work out ow muc it will cost Liam to uy enoug carpet to cover te floor. 3 Liy wants to uy some grass seed so tat se can sow a new lawn in er garden. Se wants te lawn to e a rectangle measuring 3. metres y.5 metres. Se needs 35 grams of lawn seed for every square metre of lawn. One ox of lawn seed contains 50 g. a How many oxes of lawn seed will Liy need to uy? How muc lawn seed will e left over? AO AO D 4 Find te area of te following sapes. a c AO C 5 Work out te saded area in eac diagram. a c 5 mm AO m 1 cm 7 mm 0 cm 9 mm 145
7 Exam review Self-assessment cecklist I can: find te perimeter of a D sape [p.140] find te area of a rectangle, wen given te lengt, l, and te widt, w, using te formula A l w [p.14] find te area of a square, wen given te lengt, l, using te formula A l [p.14] find te area of a triangle, wen given te ase,, and vertical eigt,, using te formula A 1_ [p.14] find te area of a parallelogram, wen given te ase,, and te vertical eigt,, using te formula A [p.14] find te area of a trapezium, wen given te lengts of te parallel sides, a and, and te distance etween te parallel sides,, using te formula A 1_ (a ) [p.14] find te area of more complicated sapes y splitting te complicated sape into easier sapes. [p.144] Exam practice F E 1 Here is a rectangle. a Work out te perimeter of te rectangle. Work out te area of te rectangle. 0 cm A carpet 60 cm wide is to e used to cover a rectangular floor measuring 4 metres y 9 metres. Calculate te lengt of carpet needed. Nov Office regulations say te gap etween te desks sould e 900 mm to allow for weelcair users. A desk as a lengt of m and a widt of 1 m. m 1 m Six of tese desks are arranged as sown in te diagram elow. Te gap etween eac desk is 900 mm. widt lengt Wat is te total lengt and te total widt of te office space needed for tese desks? 146
8 13 PERIMETER AND AREA OF D SHAPES 4 ABC is a rigt-angled triangle. AB 7 cm, BC. Work out te area of te triangle. 7 cm A D B C June a Work out te area of tis rectangle. 4.. A square as an area of 3. Work out te lengt of one side of te square. Area 3 June Te diagram sows Ro s patio. All te corners are rigt angles. Te patio is made up of square paving stones eac 50 cm y 50 cm. Work out ow many of tese paving stones are needed to tile Ro s patio. 7 m m 1 m m 7 A room as four interior walls..5 m 8 m Door m 1 m 8 m.5 m Window 1.5 m Alesa paints te walls wit emulsion paint. Se does not paint te door. A 3 litre tin of emulsion paint covers 30 m of wall. Work out ow many 3 litre tins se needs to uy. Sow all your working. 147
9 D 8 x 6 x 3 Acieving Full Marks 3x 1 In te diagram, all measurements are in centimetres. Te lengts of te sides of te triangle are x 6 x 3 3x 1 Find an expression, in terms of x, for te perimeter of te triangle. C candidates D candidates 100% 100% To get full marks on tis question, write down te perimeter of te triangle in terms of x, in an unsimplified form first and ten simplify your expression. Give your expression in its simplest form. June 009 C AO 9 7 cm 7 cm Work out te area of te sape. Nov 008 AO 10 Te diagram sows a rectangle inside a triangle. Te triangle as a ase of 1 cm and a eigt of. Te rectangle is y. Work out te area of te region sown saded in te diagram. 1 cm Nov 006 AO 11 cm cm cm Te diagram sows 3 small rectangles inside a large rectangle. Te large rectangle is y. Eac of te 3 small rectangles is y cm. Work out te area of te region sown saded in te diagram. June
10 13 PERIMETER AND AREA OF D SHAPES 1 75 m C 30 m 100 m 160 m Te diagram sows te plan of a field. Te farmer sells te field for 3 per square metre. Work out te total amount of money te farmer sould get. Marc Mrs Kunal s garden is in te sape of a rectangle. Part of te garden is a patio in te sape of a triangle. Te rest of te garden is grass. 1 m grass 7 m patio Mrs Kunal wants to spread fertiliser over all er grass. One ox of fertiliser is enoug for of grass. How many oxes of fertiliser will se need? You must sow your working. Nov Te diagram sows a garden wit a pond. Te pond is in te sape of a triangle. George is going to cover te saded area wit gravel. 35 kg of gravel is needed to cover 1 m. How muc gravel does George need? 7 m 4 m 8 m 15 A piece of card is in te sape of a trapezium. AO 7 cm A ole is cut in te card. Te ole is in te sape of a trapezium. Work out te area of te saded region. Marc
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