Question

the base of an isosceles triangle is 12 cm,if the perimeter is 32 cm,find the area

Answer 1

THANKS FOR THE QUESTION !

______________________________

ANS :

......................... 40 CM^2 ......................

______________________________

BASE OF AN ISOSCELES TRIANGLE :

=> 12 CM

______________________________

PERIMETER OF AN ISOSCELES TRIANGLE :

=> 32 CM

______________________________

=> TO FIND AREA FIRSTLY WE NEED LENGTH OF EQUAL SIDES OF AN ISOSCELES TRIANGLE

______________________________

PERIMETER OF AN ISOSCELES TRIANGLE :

=> 2 ( EQUAL SIDES ) + LENGTH OF BASE

=> 2 ( EQUAL SIDES ) + 12

______________________________

=> PERIMETER = 32CM

______________________________

32 = 2 ( EQUAL SIDES ) + 12

=> 2 ( EQUAL SIDES ) = 32 - 12

=> 2 ( EQUAL SIDES ) = 20

=> EQUAL SIDE = 20 / 2

=> EQUAL SIDE = 10 CM

______________________________

=> TO FIND AREA HEIGHT OF AN TRIANGLE IS NEEDED

______________________________

HEIGHT :

=> FORMULA :

=> √ ( EQUAL SIDE ) ^ 2 - ( BASE ) ^ 2 / 4

=> √ ( 10 ) ^ 2 - ( 12 ) ^ 2 / 4

=> √ 100 - 144 / 4

=> √ 100 - 36

=> √ 64

=> 8 CM

______________________________

AREA OF AN ISOSCELES TRIANGLE :

=> FORMULA :

=> 1/2 * BASE * HEIGHT

=> 1/2 * 10 * 8

=> 10 * 4

=> 40 CM^2

______________________________

HOPE IT WILL HELP U ......

THANKS AGAIN ......

______________________________

Answer 2

$<b >Hey here is your answer$

As we know that isosceles triangle have two equal sides . here base is given = 12 cm let the other sides = x

perimeter of triangle =

12 cm + x + x = 32 cm

2x + 12 cm = 32 cm

2x = 32 - 12 cm

x = 20 / 2 cm

x = 10 cm

So , sides of isosceles triangle are 10 cm , 10 cm and 12 cm.

s = half of the perimeter

16 cm

area =

√s(s - a)(s - b)(s - c)

√16(16 - 12)(16 - 10)(16 - 10)

√16 × 4 × 6 × 6

√2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 2 × 3

√2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3

2 × 2 × 2 × 2 × 3

48 cm²

Hope this will help you