The base of isosoceles triangle is 30. Then find the area
Answers
Correct Question :
The base of a Right - Angled Isoceles triangle is 30 cm. Then find the Area.
AnswEr :
⋆ See the First Diagram of ∆ ABC.
- BC = 30 cm,
- Assuming Right Angle ∠A = 90° and AB = AC = a [ Equal Sides ]
• Using Pythagoras Theorem :
⇝ AB² + AC² = BC²
- Plugging the Values
⇝ ( a )² + ( a )² = ( 30 cm )²
⇝ a² + a² = 900 cm²
⇝ 2a² = 900 cm²
- Dividing Both term by 2
⇝ a² = 450 cm² — eq.( I )
• Now Area of Triangle will be :
⇒ Ar. of (∆ ABC) = 1 / 2 × Base × Height
⇒ Ar. of (∆ ABC) = 1 / 2 × AB × AC
⇒ Ar. of (∆ ABC) = 1 / 2 × a × a
⇒ Ar. of (∆ ABC) = 1 / 2 × a²
- Using Value from eq.( I )
⇒ Ar. of (∆ ABC) = 1 / 2 × 450 cm²
⇒ Ar. of (∆ ABC) = 225 cm²
∴ Area of Isosceles Triangle is 225 cm².
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⋆ Now See the Second Diagram of ∆ ABC.
- Assuming Right Angle ∠B = 90°
- BC = AB = 30 cm [ Equal Sides ]
- Two Opposite Sides of Isosceles Triangles are Equal.
• Now Area of Triangle will be :
⇒ Ar. of (∆ ABC) = 1 / 2 × Base × Height
⇒ Ar. of (∆ ABC) = 1 / 2 × BC × AB
⇒ Ar. of (∆ ABC) = 1 / 2 × 30 cm × 30 cm
⇒ Ar. of (∆ ABC) = 15 cm × 30 cm
⇒ Ar. of (∆ ABC) = 450 cm²
∴ Area of Isosceles Triangle is 450 cm².
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◑ Conculsions : Area of Isosceles Triangle ABC can be 225 cm² as well as 450 cm² depending on which side you'll take as 30.
