Question

The sides of a triangle are 10 cm,4.5cm,10.5cm. Find the area of the triangle using heron's formula.

Answer 1

ϙᴜᴇsᴛɪᴏɴ:-

The sides of a triangle are 10 cm,4.5cm,10.5cm. Find the area of the triangle using heron's formula.

Solution:-

Given:-

• The sides of a triangle are 10 cm,4.5cm, 10.5cm

Find:-

• The area of the triangle using heron's formula.

Explanation:-

Let, In ∆ABC

• AB = 10 cm
• BC = 4.5 cm
• CA = 10.5

★Semiperimeter(S) = (AB+BC+CA)/2

➥ Semiperimeter (S) = (10+4.5+10.5)/2

➥ Semiperimeter (S) = 25/2 cm

➥ Semiperimeter (S) = 12.5 cm

Heron's Formula

★ Area of ∆ ABC = √[S(S-AB)(S-BC)(S-CA)]

➥ Area of ∆ ABC = √[12.5(12.5-10)(12.5-4.5)(12.5-10.5)]

➥ Area of ∆ ABC = √[12.5(2.5 × 8 × 2 )]

➥ Area of ∆ ABC = √[(12.5 × 40)]

➥ Area of ∆ ABC = √(500.0)

➥ Area of ∆ ABC = 10√5 cm².

Hence:-

• Area of ∆ ABC = 10√5 cm².

Answer 2

❗ Refer To Attachment ❗