Question

In the following figure, ABCD is a rectangle and DEC
is an equilateral triangle. Find the area of the shaded
region.
Pls solve it fast..
​

Answer 1

Given :

• ABCD is a Rectangle and DEC is an equilateral triangle .

To Find :

• Area of Shaded Region .

Solution :

Firstly we'll find the Area of Rectangle :

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Rectangle=l\times{b}}$

Putting Values :

$\longmapsto\tt{6\times{8}}$

$\longmapsto\tt{48\:{cm}^{2}}$

Now , We'll calculate the Area of Equilateral Triangle :

$\longmapsto\tt\bf{Each\:Side=6\:cm}$

Using Formula :

$\longmapsto\tt\boxed{Area\:of\:Equilateral\:Triangle=\dfrac{\sqrt{3}}{4}\times{a}^{2}}$

Putting Values :

$\longmapsto\tt{\dfrac{\sqrt{3}}{4}\times{(6)}^{2}}$

$\longmapsto\tt{\dfrac{\sqrt{3}}{{\cancel{4}}}\times{{\cancel{36}}}}$

$\longmapsto\tt{\sqrt{3}\times{9}}$

$\longmapsto\tt\bf{15.6\:{cm}^{2}\:(Approx.)}$

Now ,

Area of Shaded Region :

$\longmapsto\tt{48-15.6}$

$\longmapsto\tt\bf{32.4\:{cm}^{2}}$

Answer 2

• Area of shaded region = (48 - 9√3) cm²

━━━━━━━━━━━━━━━━━━━━━━━━━━

Explanation :

G I V E N :

• An equilateral triangle DEC with side = 6 cm
• A rectangle ABCD with dimensions (L × B) = 8 cm × 6 m.

T OㅤF I N D :

• Area of shaded region = ?

S O L U T I O N :$\:$

✇ Finding area of rectangle ABCD :

➵ Area (rectangle ABCD) = L × B

➵ Area (rectangle ABCD) = 8 × 6

➵ Area (rectangle ABCD) = 48 cm² ㅤ(ℹ)

✇ Finding area of triangle DEC :

➵ Area (triangle DEC) = √3/4(side)²

➵ Area (triangle DEC) = √3/4(6)²

➵ Area (triangle DEC) = √3/4 × 6 × 6

➵ Area (triangle DEC) = √3/2 × 3 × 6

➵ Area (triangle DEC) = √3 × 3 × 3

➵ Area (triangle DEC) = √3 × 9

➵ Area (triangle DEC) = 9√3 cm²ㅤㅤ (ℹℹ)

✇ Finding area of shaded region :

➵ Area (shaded region) = (ℹ) - (ℹℹ)

➵ Area (shaded region) = (48 - 9√3) cm²

∴ Hence, area of shaded region = (48 - ㅤ9√3) cm²

━━━━━━━━━━━━━━━━━━━━━━━━━━