# The base of an isosceles triangle is 4cm and its perimeter is 20cm. Find the area

↵base = 4
perimeter = 20
isosceles has two sides equal
so, 20 = x + x+ 4
20 = 2x + 4
16  = 2x
16 = x
2
8= x
by using heron's formula
side a = 4cm
side b = 8cm
side c = 8cm
semi perimeter = side a + side b + side c
2

=  4 + 8 + 8
2

=  10
heron's formula = (root of) ​√s (s-a)(s-b)(s-c)           (s-a) = 10 - 4 = 6
(s-b) = 10 - 8 = 2
(s-c) = 10 - 8 = 2
√ 10 * 6 *2*2
2 √10 * 6
2 √2*5 * 2*3
2* 2 √15
​4√15
​(√15 = 3.87)
4 * 3.87
=15.48 cm² (approximate)

• 5
Let the unknown side be "x"
2x +4 = 20. ( The 2 opposite sides are equal in an isosceles triangle) ( sum of sides is the perimeter)
2x = 20-4
2x= 16
x = 8.
therefore, the Unknown side is 8cms.

• -1
4√15 sq.cm
• 0
this can be find out as
let it be triangle abc
sides of triangle = perimeter of triangle
sides of triangle = base = 4 cm
bc = base = 4cm
ab = ac as it is an isosceles triangle
so ab + ac + bc = 20
ab + ab + 4cm = 20 cm
2ab + 4cm = 20
2ab = 16cm
ab = 16/2
ab = 8cm
and now you have got the sides so you can find out the area by herons formulae
• 0
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