Question

ind the area of a rhombus, each side of which measures 20 cm and one of whose diagonals is
24 cm.
275

Answer 1

Answer:

the area of the rhombus

$2 \sqrt{32 (32 - 20) {}^{2}( 32 - 24} ) \\ = 2 \sqrt{32 \times 12 \times 12 \times 8} \\ = 2 \sqrt{8 \times 4 \times 4 \times 3 \times 4 \times 3 \times 8} \\ = 2 \times 8 \times 4 \times 2 \times 3 \\ = 384 \: \: cm {}^{2}$

Answer 2

$\bold{\Huge{\underline{\boxed{\sf{\green{ANSWER\::}}}}}}$

$\bold{\Large{\underline{\sf{\pink{Given\::}}}}}$

In a rhombus each side of which measures 20cm & one of whose diagonal is 24cm.

$\bold{\Large{\underline{\rm{\red{To\:find\::}}}}}$

The area of rhombus.

$\bold{\Large{\underline{\sf{\orange{Explanation\::}}}}}$

We know that formula of the area of rhombus:

→ $\bold{\frac{1}{2} *d1*d2}$

&

$\bold{We\:have\begin{cases}\sf{Length\:of\:side\:of\:rhombus=20cm}\\ \sf{Length\:of\:one\:diagonal=24cm}\end{cases}}}$

In ΔAOB,

Using Pythagoras Theorem:

→ [Hypotenuse]² = [Base]² + [Perpendicular]²

→ AB² = OA² + OB²

→ 20² = 12² + OB²

→ 400 = 144 + OB²

→ OB² = 400 - 144

→ OB² = 256

→ OB = √256

→ OB = 16cm

∴The length of other diagonal,[d2] = 2OB = 2×16 = 32cm

Now,

⇒ Area = $\bold{\frac{1}{2} *d1*d2}$

⇒ Area = $\bold{(\frac{1}{2} *24*32)cm^{2} }$

⇒ Area = $\bold{(\frac{1}{\cancel{2}} *\cancel{24}*32)cm^{2} }$

⇒ Area = (12×32)cm²

⇒ Area = 384cm²

Thus,

The area of a rhombus is 384cm².