Question

An isosceles triangle has perimeter 20 cm and each of equal sides is 8 cm. Find area of

the triangle.​

Answer 1

◉Question◉

☛An isosceles triangle has perimeter 20 cm and each of equal sides is 8 cm. Find area of the triangle.

◉Answer◉

☛Given data are as follows:

• Perimeter of triangle = 20 cm
• Equal sides = 8cm

☛To find:

• Area of triangle.

◉Refer the attachment for diagram.

$\large{ \sf{ \mapsto{perimeter \: of \: triangle = sum \: of \: sides \: of \: \triangle}}} \\ \\ \large{ \sf{ \star{ \green{ \: here \: for \: isoceles \: \: \triangle}}}} \\ \\ \large{ \sf{ \mapsto{perimeter = 2(equal \: side) + base}}} \\ \\ \large{ \sf{ \mapsto{20 \: cm = 8 \: cm + 8 \: cm + base}}} \\ \\ \large{ \sf{ \mapsto{base = 20 - 16 \: cm}}} \\ \\ \large{ \sf{ \mapsto{ \boxed{ \purple{base = 4 \: cm}}}}}$

☛ Now, for finding area of triangle.

We will use Heron's formula,

$\large{ \boxed{ \sf{area \: of \: \triangle \: = \: \sqrt{s(s - a)(s - b)(s - c)} }}} \\ \\ \large{ \sf{ where \: \: \: s = semiperimeter}} \\ \large{ \sf{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{perimeter}{2} }} \\ \\ \large{ \sf{and \: a \: \: b \: \: and \: \: c \: are \: the \: sides}}$

☛By using the formula

$\large{ \sf{ \star{ \: \: s = \frac{20}{2} = 10 \: cm}}} \\ \\ \large{ \sf{ \mapsto{area = \sqrt{10(10 - 8)(10 - 8)(10 - 4) } {cm}^{2} }}} \\ \\ \large{ \sf{ \mapsto{area = \sqrt{10(2)(2)(6)} {cm}^{2} }}} \\ \\ \large{ \sf{ \mapsto{area = \sqrt{2 \times 5 \times 2 \times 2 \times 2 \times 3}</strong><strong>cm</strong><strong>^</strong><strong>2</strong><strong> }}} \\ \\ \large{ \sf{ \mapsto{area = 2 \times 2 \sqrt{5 \times 3} \: {cm}^{2} }}} \\ \\ \large{ \sf{ \mapsto{area = 4 \sqrt{15} {cm}^{2} }}} \\ \\ \large{ \sf{ \star{ \boxed{ \green{area = 15.5 \: {cm}^{2} }}}}}$

◉So final answer◉

$\huge{ \boxed{ \bold{ \red{ = 15.5 \: {cm}^{2} }}}}$