Question

Two equal sides of an isosceles triangle are 10 cm and the perimeter is 28 cm, then the area of the triangle is​

Answer 1

Answer:

$8 \sqrt{21} \: \: \: {cm}^{2} .$

Step-by-step explanation:

$s = 14 \: cm. \\ \\ x = 10 \: cm \\ \\ y = 10 \: cm \\ \\ z = 28 - 1 0- 10 \\ \\ z = 28 - 20 \\ \\ z = 8 \: cm. \\ \\ area \: of \: triangle \: = \: \sqrt{(s)(s - a)(s - b)(s - c)} \\ \\ = \sqrt{14(14 - 10)(14- 10)(14- 8)} \\ \\ = \sqrt{14 \times 4 \times 4 \times6 } \\ \\ = \sqrt{7 \times 2 \times {4}^{2} \times 3 \times 2 } \\ \\ = 4 \times 2 \sqrt{7 \times 3} \\ \\ = 8 \sqrt{21} \: \: \: {cm}^{2} .$

Answer 2

Step-by-step explanation:

Given

• The perimeter of triangle = 28 cm.
• Two equal side of an Isosceles triangle is 10 cm.

To Find :

The area of triangle

Solution :

${\implies{\sf{Perimeter \: of \: {Triangle} = a + b + c}}} \\ {\implies{\sf{28= 10 + 10 +c}}} \\ {\implies{\sf{28= 20 + c}}} \\{\implies{\sf{c = 28 - 20}}} \\ {\implies{\sf{\red{c =8 \: cm}}}}$

Hence, the third angle of triangle is 8 cm.

Now , area of the triangle

$\begin{gathered}\begin{gathered} \small {\underline{\underline{\sf{\purple{Here :}}}}}\begin{cases} \sf{a = 10 \: cm} \\ \sf{b = 10 \: cm} \\ \sf{c = 8\: cm} \end{cases} \end{gathered}\end{gathered}$

Now , we have to find semi perimeter

$\implies{\sf{Semi \: Perimeter = \dfrac{a + b + c}{2}}}$

$\implies{\sf{Semi \: Perimeter = \dfrac{10 + 10 + 8}{2}}}$

$\implies{\sf{Semi \: Perimeter = \dfrac{28}{2}}}$

$\implies{\sf{Semi \: Perimeter = \cancel{\dfrac{28}{2}}}}$

$\implies{\sf{ \purple{Semi \: Perimeter = 14 \: cm}}}$

Hence, the semi perimeter of triangle is 14 cm.

Now, the area of tiangle

${\rightarrow{\sf{Area \: of \: {Triangle} = \sqrt{s(s - a)(s - b)(s - c)}}}}$${ \rightarrow{\sf{Area \: of \: {Triangle} = \sqrt{14(14 - 10)(14 - 10)(14 - 8)}}}}$${\rightarrow{\sf{Area \: of \: {Triangle} = \sqrt{14(4)(4)(6)}}}}$${ \rightarrow{\sf{Area \: of \: {Triangle} = \sqrt{14 \times 4 \times 4 \times 6}}}}\\{\rightarrow{\sf{Area \: of \: {Triangle} = \sqrt{1344}}}}$${\rightarrow{\sf{\purple{Area \: of \: {Triangle} = 36.66 \: {cm}^{2}}}}}$

Hence, the area of triangle is 36.66 cm².