Heron’s formula maths presentation

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question no.1,2 and 3 of Ex 12.2 of NCERT book.

Transcript of Heron’s formula maths presentation

  • 1. HERONSFORMULA

2. EXERCISE 12.2Q1 A park in the shape of quadrilateral ABCD , has C= 90, AB = 9m , BC = 12m, CD = 5m and AD = 8m.How much area does it occupy?A8 mD9m5 mB 12 mC 3. SOLUTIONArea of BCD = BC CD= ( 12 5 ) m= 30 cmUsing Pythagoras theorem, we haveBD = BC + CDBD = 12 + 5BD = 144 + 25BD = 169BD = 169 = 13 m 4. For ABDLet a = 13m, b = 8m and c = 9mNow, s = ( a + b + c)= ( 13 + 8 + 9) m= 30m= 15 ms a = (15 -13) m = 2ms b = (15 - 8) m = 7 ms c = (15 9) m = 6 mand Area of ABD = s(s a)(s b)(sc)= 15 2 7 6 m= 3 5 2 7 2 3 m 5. = 2 2 3 3 5 7 m= 2 335 m (approx.)= 6 5.9 m (approx.) Required area = ABD +BCD= 35.4 m + 30 m= 65.4 m 6. Q2 Find the area of a quadrilateral ABCD inwhich AB = 3 cm, CD = 4 cm, DA = 5 cm, andAC = 5 cm.5 cmC4 cm3 cmDA B 7. SOLUTIONArea of ABC = AB BC= ( 3 4) cm= 6 cmFor ACD:Let a = 5 cm, b = 4 cm and c = 5 cm.then,s = (a + b + c)s = ( 5 + 4 + 5 ) cms = 14 cms = 7 cm 8. Now, s a = ( 7 5 ) = 2 cms b = ( 7 4 ) = 3 cms c = ( 7 5 ) = 2 cmArea of ACD = s(s a)(s b)(sc)= 7 (2) (3) (2)= 2 2 3 7= 2 3 7= 2 21= 2 4.58 = 9.167 /-Area of quadrilateral ABCD = Area of ABC +Area of ACD= 6 + (9.16) cm= 15.2 cm (approx.) 9. Q3 Radha made a picture of aeroplane withcoloured paper as shown in Fig. 17.24. findthe total area of the paper used.6 cm 6 cmIII5 cm6.5 cm1.5 cm1 cm 1 cm2 cmIVVIII 10. SOLUTIONArea of region I :Region I is enclosed by a triangle of sides a = 5 cm, b = 5 cm and c =1 cm