Question

An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find
the area of the triangle.
​

Answer 1

Answer: 9 x root 15

Step-by-step explanation:

1.  by pythagorean theorem and then finding area

let the triangle be triangleABC, where A is the point where the equal sides meet

each of the equal sides = 12

total perimeter=30

base= 30 - (12 x 2)

base= 30 - 24

base = 6cm

draw a median from dividing the base

now,

since the median and altitude are the same here,

taking the point of intersection as D,

triangle ADB is a right angle triangle

also, by pythagorean theorem,

AD^2=AB^2 + BD^2

AD^2=(12)^2 + (3)^2 [BD = half of BC]

AD^2=124 + 9

AD^2=133

AD= square root of 133

area = 1/2 x root 133 x 6

area=9 x root 15

2.  by herons formula

from 1 we learnt that base =6 cm

perimeter = 30 cm

semi-perimeter[S]=30/2=15cm

herons formula: area of triangle = root(s(s - a)(s - b)(s - c))

area= root(15(15 - 12)(15-12)(15 - 6))

area= root 1215

1215     3

405      3

135       5

27          3

9              3

3               3

=9 x root15

Answer 2

Step-by-step explanation:

Perimeter of Isosceles Triangle = 30cm

Length of Each Equal Side = 12cm

We know that an isosceles Triangle Has 2 equal sides...

Length of Two Equal sides = 12cm×2 = 24cm

Now length of the unequal side = 30cm - 24cm = 6cm

By Heron's Formula Area of Triangle = sqrt. s(s-a)(s-b)(s-c)

Where 's' is the semi perimeter of the triangle and

S = (a+b+c)/2 and (a,b,c) are the sides of the triangle.

S = (12cm+12cm+6cm)/2 = 30cm÷2 = 15cm

Now Area of Triangle = sqrt. 15(15-12)(15-12)(15-6)(cm²)

= sqrt. 15×3×3×9×cm² = sqrt. 1215cm²

= 34.8568501159

~ 35cm²

So the Area of Triangle is 35cm²...

Hope this helps you