An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm .Find the area of the the triangle using the Herons Formula .
Answers
Answer:
In the above formula, “s” represents the semi – perimeter of the triangle, “a, b and c” represents the sides of the triangle ABC. Perimeter of the triangle is given as 30 cm so the semi perimeter is equal to half of the perimeter i.e. 15 cm. Hence, the area of the triangle is equal to 9√15cm2.
Step-by-step explanation:
Perimeter of isosceles triangle=30cm
Length of equal sides=12cm
Let third side of triangle=xcm
According to problem,
x+12+12=30
x+24=30
x=30−24
x=6
∴ Third side of triangle=6cm
Using Heron's formula
Area of triangle=
s(s−a)(s−b)(s−c)
sq. units
where s=
2
a+b+c
s=
2
30
=15
Area of triangle=
15(15−12)(15−12)(15−6)
cm
2
=
15×3×3×9
cm
2
=3×3×
15
cm
2
=9
15
cm
2
∴ Area of triangle=9
15
cm
2
.
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