Question

*10 सेमी बाजूच्या समभुज चौकोनाचा एक कर्ण 16 सेमी असल्यास चौकोनाचे क्षेत्रफळ किती?*

1️⃣ 80 चौसेमी
2️⃣ 128 चौसेमी
3️⃣ 48 चौसेमी
4️⃣ 96 चौसेमी​

Answer 1

Given : 10 सेमी बाजूच्या समभुज चौकोनाचा एक कर्ण 16 सेमी असल्यास

Rhombus with side 10 cm having one diagonal 16 cm

To Find :  चौकोनाचे क्षेत्रफळ

Area of the rhombus

1️⃣ 80 चौसेमी

2️⃣ 128 चौसेमी

3️⃣ 48 चौसेमी

4️⃣ 96 चौसेमी

Solution:

One diagonal is 16 cm

side is 8 cm

Diagonals of rhombus bisects each other perpendicularly

Let say other diagonal is 2d

Then  ( 2d/2)²  + (16/2)²   = 10²

=> d²  + 8² = 10²

=> d = 6

=> 2d = 12

Hence other diagonal is 12 cm

Area of rhombus = (1/2) * product of diagonals

= (1/2) * 16 * 12

= 96

4️⃣ 96 चौसेमी​

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Answer 2

Given :-

• Side of rhombus = 10 cm.
• Diagonal of rhombus = 16 cm.

To Find :-

• Area of rhombus = ?

Answer :-

As we know that,

• Diagonals of a rhombus bisect each other at 90° .

Let us assume that , diagonal of other diagonal is 2x cm .

So,

→ (D1/2)² + (D2/2)² = (side)²

→ (2x/2)² + (16/2)² = 10²

→ x² + 8² = 100

→ x = √(100 - 64)

→ x = 6 cm .

then,

→ Diagonal of other diagonal = 2x = 2 * 6 = 12 cm.

therefore,

→ Area of rhombus = (1/2) * D1 * D2 = (1/2) * 16 * 12 = 96 cm². (Ans.)

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