Question

1. Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is
42cm​

Answer 1

Answer:

A≈69.65cm²

a Side

18

cm

b Base

10

cm

P Perimeter

42

cm

Using the formulas

A=s(s﹣a)(s﹣b)(s﹣c)

P=a+b+c

s=a+b+c

2

Solving forA

A=1

4﹣P4+4P3a+4P3b﹣4(Pa)2﹣12P2ab﹣4(Pb)2+8Pa2b+8Pab2=1

4·﹣424+4·423·18+4·423·10﹣4·(42·18)2﹣12·422·18·10﹣4·(42·10)2+8·42·182·10+8·42·18·102≈69.64912cm²

Answer 2

Answer:

3rd side is 42-(10+18)

i. e. 14

so according to herons formula

√(s(s-a) (s-b) (s-c)) =area of triangle

s is semi perimetre

i. e. s=perimetre/2

s=42/2=21

√(21(21-14) (21-18) (21-10))

√3(7) (7) (3) (11)

3(7) *√11

21√ 11 is the area or 69.6491