Question

An isosceles triangle has a base 6cm long and one of the equal sides is 5cm long. Find the area of the triagle

Answer 1

Answer:

12 cm²

Step-by-step explanation:

$\text{Given two equal sides of triangle, 5 cm each and an unequal side = 6 cm.}\\\\\text{Thus, area of triangle = } \sqrt{s((s-a)(s-b)(s-c)},\\\\\text{Where, a, b and c are the three sides of the triangle. Here, since it is an isosceles triangle, a = b}$

$\text{And, s is the semiperimeter = } \dfrac{a+b+c}{2} \: \: or \: \dfrac{2a + c}{2} \: \text{in this case.}\\\\\text{Thus, area = } \sqrt{s(s-a)(s-a)(s-c)}\\\\\text{a = 5 cm; b = 6 cm; s = } \dfrac{2(5) + 6}{2} = \dfrac{10+6}{2}\\\\\implies s = \dfrac{16}{2} = 8 \: cm\\\\\\\text{Now, finally, area of triangle}\\\\= \sqrt{s(s-a)(s-a)(s-c)}\\\\= \sqrt{8(8-5)(8-5)(8-6)}\\\\= \sqrt{8 \times 3 \times 3 \times 2}\\\\= \sqrt{144}\\\\= \boxed{12 \: cm^2}$

Hope it helps.