Question

3. Find the area of a triangle whose sides are: (a) a = 8 cm, b = 11 cm, c = 13 cm,​

Answer 1

Answer:

Area of the triangle is 43.82 cm² (approx).

Step-by-step explanation:

Given :

• Sides of triangle, a, b and c are 8 cm, 11 cm and 13 cm respectively.

To find :

• Area of the triangle.

Solution :

We know,

Heron's formula :

• Area of triangle = √[s(s - a)(s - b)(s - c)]

[Where, s is semi-perimeter, a , b and c are sides of triangle]

So,

• Semi-perimeter (s) = Perimeter of triangle/2

We know that, Perimeter of triangle = Sum of all sides of triangle.

$\implies$ s = (a + b + c)/2

$\implies$ s = (8 + 11 + 13)/2

$\implies$ s = 32/2

$\implies$ s = 16

Semi-perimeter (s) is 16 cm.

Now,

$\implies$ Area = √[16(16 - 8)(16 - 11)(16 - 13)]

$\implies$ Area = √(16 × 8 × 5 ×3)

$\implies$ Area = √(2 × 2 × 2 × 2 × 2 × 2 ×2 × 5 × 3)

$\implies$ Area = 2 × 2 × 2 × √(2 × 5 × 3)

$\implies$ Area = 8√30

• √30 = 5.477.

$\implies$ Area = 8 × 5.477

$\implies$ Area = 43.82

Therefore,

Area of triangle is 43.82 cm² (appox).

Answer 2

Answer:

$\huge\mathfrak\color{0000FF}Answer$

Step-by-step explanation:

$\sf First\:find\:the\:perimeter\:of\:given\:triangle[\tex][tex]\sf \: perimeter \: of \: triangle \: = all \: sides \: of \: triangle \\ \sf \: = 8 + \: 11 + 13 \\ \sf \: = 32 \\ \sf \: then \: find \: s \\ \sf \: s \: = \frac{p}{2} \\ \sf \: = \frac{32}{2} \\ \sf \: = 16 \\ \sf \: by \: herons \: formula \: \\ \sf \sqrt{s(s - a)(s - b)(s - c)} \\ \sf \: where \: a \: b \: and \: c \: are \: the \: sides \: of \: \\ \sf \: triangle \: \\ \sf \: = 16(16 - 8)(16 - 11)(16 - 13) \\ \sf = \sqrt{16 \times 8 \times 5 \times 3} \\ \sf = \sqrt{128 \times 5 \times 3} \\ \sf \: = \sqrt{640 \times 3} \\ \sf \: = \sqrt{1920}$

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