Q. 2 Find the area of a triangle whose sides are 4.5 cm and 10 cm and perimeter 10.5 cm. a) 4.5 b) 5.5 c) 2 d) 2.5
Answers
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Step-by-step explanation:
The area of the triangle is 3\sqrt { 14 } cm^23
14
cm
2
.
Step-by-step explanation:
Let a, b and c be the three sides of the triangle. Here, a=4.5 cm, b=10 cm and c=?
∴ Semi perimeter =\frac { a+b+c }{ 2 }
2
a+b+c
⇒\frac { (4.5+10+c) }{ 2 } =10.5
2
(4.5+10+c)
=10.5
⇒14.5 +c = 2 \times 10.5 = 2114.5+c=2×10.5=21
⇒c = 21 - 14.5 = 6.5 cmc=21−14.5=6.5cm
∴ Area of triangle (Using Heron's formula) =\sqrt { (s(s-a)(s-b)(s-c)) }=
(s(s−a)(s−b)(s−c))
Square units \begin{gathered}=\sqrt { 10.5 (10.5-10) (10.5-4.5) (10.5-6.5)} cm^2 \\=\sqrt{10.5 (0.5) (6) (4)} cm^2\end{gathered}
=
10.5(10.5−10)(10.5−4.5)(10.5−6.5)
cm
2
=
10.5(0.5)(6)(4)
cm
2
=\sqrt {(10.5\times12)} cm^2 =\sqrt {126} cm^2 =\sqrt{ (14\times9)} cm^2 =3\sqrt{14} cm^2=
(10.5×12)
cm
2
=
126
cm
2
=
(14×9)
cm
2
=3
14
cm
2
Hence, Area of triangle =3\sqrt { 14 } cm^23
14
cm
2
.