Triangle ka area

Rectangle ko diagonal se kaatne pe kya hota hai?

Ek rectangular kaagaz lo aur ek kone se saamne wale kone tak line kheencho. Ye line diagonal hai. Isse kaato to do triangles milenge.

Ab ek triangle ko doosre ke upar rakho. Dono ek-doosre ko bilkul dhak lete hain, yaani dono ka area same hai. Dono triangles milkar poora rectangle banate hain, isliye har triangle ka area rectangle ka aadha hai. Lambe, chhote rectangles aur squares sab ke saath try karo: har baar yahi hoga.

Kya rectangle mein har triangle uska aadha hota hai?

Triangle rectangle ka aadha tab gherta hai jab:

• triangle ki ek side rectangle ki ek poori side ho (uska base), aur
• triangle ka teesra kona saamne wali side pe kahin bhi ho.

Kyun? Upar wale kone se base tak seedhi line kheencho. Ye rectangle ko do chhote rectangles mein, aur triangle ko do hisson mein baant deti hai. Har hissa ek chhote rectangle ka aadha hai. Aadha + aadha = poore rectangle ka aadha.

Grid paper pe ek worked example

Grid paper pe ek rectangle 6 units lamba aur 4 units ooncha hai, to uska area 6 × 4 = 24 sq units hai.

1. Diagonal wala triangle: 24 ka aadha = 12 sq units.
2. Triangle jiska upar wala kona, upar wali side pe baayein se 2 units pe hai: dashed line rectangle ko 2 × 4 aur 4 × 4 ke hisson mein baantti hai. 8 ka aadha + 16 ka aadha = 4 + 8 = 12 sq units.

Dono triangles bahut alag dikhte hain, lekin dono rectangle ka theek aadha gherte hain: 12 sq units.

Do aur chhote examples

• Diagonal se kata square: 8 cm side wale square ka area 8 × 8 = 64 sq cm hai, to har triangle 64 ka aadha = 32 sq cm.
• 10 cm × 6 cm rectangle mein triangle, jiska upar wala kona baayein se 3 cm pe hai: kone se neeche aati line 3 × 6 aur 7 × 6 ke hisse banati hai. 18 ka aadha + 42 ka aadha = 9 + 21 = 30 sq cm, jo 60 ka aadha hai, bilkul jaisa hona chahiye.

Rectangles aur triangles se bani shapes ka area kaise nikaalein?

Shape ko aise tukdon mein todo jinka area nikaal sako, phir jod do.

Example: ek shape 4 cm × 3 cm rectangle hai jiske upar ek triangle hai. Triangle ka base rectangle ki 4 cm wali upar ki side hai, aur uski choti 2 cm upar hai.

• Rectangle: 4 × 3 = 12 sq cm.
• Triangle: 4 cm × 2 cm rectangle ka aadha = 8 ka aadha = 4 sq cm.
• Kul area = 12 + 4 = 16 sq cm.

Grid paper pe gin bhi sakte ho: poore squares 1, aur jo squares tirchi line se theek aadhe kate hon, wo ½.

Triangles kyun zaroori hain?

Hamare aas-paas ki kai shapes, jaise chhat, patang, jhande aur zameen ke plot, rectangles aur triangles mein todi ja sakti hain. In dono ka area nikaalna aa gaya, to seedhi sides wali lagbhag har shape ka area nikaal sakte ho. Aage badhne se pehle rectangle aur square ka area revise karo, kyunki yahan har triangle ka area ek rectangle se shuru hota hai.