NCERT Class 9 Mathematics
CONSTRUCTIONS 193 Construction 11.5 : To construct a triangle given its base, a base angle and the difference of the other two s ...
194 MATHEMATICS Construction 11.6 : To construct a triangle, given its perimeter and its two base angles. Given the base angles, ...
CONSTRUCTIONS 195 Example 1 : Construct a triangle ABC, in which ✄B = 60°, ✄ C = 45° and AB + BC CA = 11 cm. Steps of Construc ...
196 MATHEMATICS 11.4 Summary In this chapter, you have done the following constructions using a ruler and a compass: To bisect ...
CHAPTER 12 HERON’S FORMULA 12.1 Introduction You have studied in earlier classes about figures of different shapes such as squar ...
198 MATHEMATICS area of ✁ABC is given by 1 2 × base × height = 1 2 × 12 × 5 cm^2 , i.e., 30 cm^2 Note that we could also take 5 ...
HERON’S FORMULA 199 Now suppose that we know the lengths of the sides of a scalene triangle and not the height. Can you still fi ...
200 MATHEMATICS s – a = (48 – 40) m = 8 m, s – b = (48 – 24) m = 24 m, s – c = (48 – 32) m = 16 m. Therefore, area of the park A ...
HERON’S FORMULA 201 Example 1 : Find the area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm (s ...
202 MATHEMATICS Example 3 : The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its perimeter is 300 m. Find its ar ...
HERON’S FORMULA 203 There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE ...
204 MATHEMATICS So, area for growing wheat = 400(400200) (400 – 240) (400 – 360)m^2 = 400 ✁200 160✁ ✁40 m^2 =16000 2 m^2 = 1.6 × ...
HERON’S FORMULA 205 The second group has to clean the area of triangle ACD, which is scalene having sides 41 m, 15 m and 28 m. H ...
206 MATHEMATICS Alternative method : Draw CE ✄ BD (see Fig. 12.14). As BD = 160 m, we have DE = 160 m ÷ 2 = 80 m And, DE^2 + CE^ ...
HERON’S FORMULA 207 A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its lo ...
CHAPTER 13 SURFACE AREAS AND VOLUMES 13.1 Introduction Wherever we look, usually we see solids. So far, in all our study, we hav ...
SURFACE AREAS AND VOLUMES 209 First we would need a rectangular piece to cover the bottom of the bundle. That would be as shown ...
210 MATHEMATICS This shows us that the outer surface of a cuboid is made up of six rectangles (in fact, rectangular regions, cal ...
SURFACE AREAS AND VOLUMES 211 Recall that a cuboid, whose length, breadth and height are all equal, is called a cube. If each ed ...
212 MATHEMATICS Length =80 cm, Breadth = 40 cm, Height = 20 cm. The surface area of the box = 2(lb + bh + hl) = 2[(80 × 40) + (4 ...
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