Question

7. Find the area of a triangle whose two sides are 8 cm and 11 cm and the perimeter is 32 cm.
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Answer 1

Answer:

Given:-

two sides of a triangle are 8cm and 11cm respectively are given.

perimeter of ∆= 32 cm.

perimeter of∆=sum of three sides

perimeter of∆=S1 + S2 + S3

32=8+11+S3

S3 = 32 - 19

S3 = 13

semi perimeter(s) = 32/2

semi perimeter (s)= 16cm

Using Herons formula

area of a triangle = √s(s-a)(s-b)(s-c)

area of a triangle = √16(16-8)(16-11) (16-13)

area of a triangle = √16(8)(5)(3)

area of a triangle = 8√30

Therefore, area of a triangle is8√30 cm^2

Answer 2

Given :-

• Perimeter of triangle = 32 cm
• Length of two sides of triangle are 8 cm and 11 cm

To Find :-

• Area of traingle = ?

Solution :-

Let the sides of traingle be a, b, c.

In Triangle,

• First side = 8 cm
• Second side = 11 cm
• Perimeter = 32 cm

Now, lets find the third side of a traingle :

→ Third side = Perimeter - (First side of ∆ - Second side of ∆)

→ Third side = 32 - (8 + 11)

→ Third side = 32 - 19

→ Third side = 13 cm

Now, we will find the Semi Perimeter of ∆ :

➻ Semi Perimeter = All sides of a ∆ ÷ 2

➻ Semi Perimeter = a + b + c ÷ 2

➻ Semi Perimeter = 8 + 11 + 13 ÷ 2

➻ Semi Perimeter = 32 ÷ 2

➻ Semi Perimeter = 16 cm

Now, lets find the area of ∆ by using herons formula :

➳ Area = √s(s - a) (s - b) (s - c)

➳ Area = √16(16 - 8) (16 - 11) (16 - 13)

➳ Area = √16 × 8 × 5 × 3

➳ Area = 8√2 × 5 × 3

➳ Area = 8√30 cm²

Therefore, the area of traingle is 8√30 cm².