A design is made up of 8 congruent triangles each having side 70 cm, 56 cm and 42 cm is painted on a circular glass window of radius 70 cm. Find the painted area of the glass window and the remaining area.
(no copied answer by internet else reported)
-best user
-moderators
-brainly ⭐
Answers
Answer:
• Painted area is 9408 cm².
• Remaining area is 5992 cm².
Step-by-step explanation:
Given :
- There are 8 congruent triangles each having sides 70 cm, 56 cm and 42 cm.
- Radius of circular glass window is 70 cm.
To find :
- Painted area of glass.
- Remaining area of glass.
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 = Perimeter/2
→ s = 56 + 42 + 70/2
→ s = 168/2
→ s = 84
Semi-perimeter is 84 cm.
Then,
→ Area = √84(84 × 56)(84 - 42)(84 - 70)
→ Area = √84 × 28 × 42 × 14
→ Area = √2 × 2 × 3 × 7 × 2 × 2 × 7 × 2 × 3 × 7 × 2 × 7
→ Area = 2 × 2 × 2 × 3 × 7 × 7
→ Area = 1176
Area of one triangular design is 1176 cm²
• Painted area of glass = Area of one triangular design × 8
→ Painted area of glass = 1176 × 8
→ Painted area of glass = 9408 cm².
Thus,
Painted area of glass is 9408 cm²
Now,
We also know,
• Area of circle = πr²
→ Area of circular glass = 22/7 × (70)²
→ Area of circular glass = 22/7 × 4900
→ Area of circular glass = 22 × 700
→ Area of circular glass = 15400
Area of circular glass is 15400 cm².
So,
• Remaining area/Unpainted area = Area of circular glass - Painted area
→ Remaining area = 15400 - 9408
→ Remaining area = 5992
Thus,
Remaining area is 5992 cm².
Answer:
Painted area= 9408 cm²
Remaining area= 5992 cm²
