Question

Find the area of an isosceles triangle whose equal sides are 6 cm each and the third side is 8 cm.

(a) 8√5 cm²
(b)5√8 cm²
(c)3√55 cm²
(d) 3√8 cm​

Answer 1

Step-by-step explanation:

so if there are two equal side then height can be found by

Pythagoras theo

so (6)^2 -( 8/2)^2 = p ^2

36 -16 = p^2

20 = p^2

p = root (20) = root (4×5)

= 2 root (5)

now area = 0.5 × b× h

= 0.5 × 8 × 2 root(5)

= 8 root (5) cm ^2

option (a) is correct one

Answer 2

Given :

• Two equal sides of an isosceles triangle are 6cm each.
• Third side of the triangle is 8cm.

To Find :

• Area of the isosceles triangle.

Solution :

• a = 6cm.
• b = 6cm.
• c = 8cm.

$\longmapsto\tt{s=\dfrac{a+b+c}{2}}$

$\longmapsto\tt{s=\dfrac{6+6+8}{2}}$

$\longmapsto\tt{s=\cancel\dfrac{20}{2}}$

$\longmapsto\tt\bold{s=10cm}$

Now ,

$\longmapsto\tt{Area=\sqrt{s(s-a)(s-b)(s-c)}}$

$\longmapsto\tt{\sqrt{10(10-6)(10-6)(10-8)}}$

$\longmapsto\tt{\sqrt{10\times{4}\times{4}\times{2}}}$

$\longmapsto\tt{\sqrt{5\times{2}\times{2}\times{2}\times{2}\times{2}\times{2}}}$

$\longmapsto\tt{2\times{2}\times{2}\sqrt{5}}$

$\longmapsto\tt\bold{8\sqrt{5}{cm}^{2}}$

So , The Area of the isosceles triangle is 8√5cm²..

Option a) 8√5cm² is correct..