Question

The area of a quadrilateral, one of whose diagonals is 30 cm long and the perpendiculars from the
other two vertices are 19 cm and 11 cm respectively is -
(A) 400 cm
(B) 450 cm
(C) 500 cm
(D) 425 cm​

Answer 1

★ Given :

Diagonals is 30 cm long and the perpendiculars from the other two vertices are 19 cm and 11 cm.

★ To find :

Area of Quadrilateral.

★ Solution :

➲Diagonals of Quadrilateral = 30 m

➲Lenght of || sides = 19, 11 cm

Ar (ABCD) = Ar(ABC) + Ar( ACD)

➤ (1/2 × 30 × 19) + (1/2 × 30 × 11)

➤ 1/2 × 30 ( 19 + 11)

➤ 15 × 30

➤ 450 cm²

∴Area of Quadrilateral is 450 cm²

_______________

Answer 2

AnsWeR :

$\large \implies \sf 450cm^2$

Solution :

Given :

• Diagonals is 30 cm long
• Two vertices are 19 cm and 11 cm respectively.

To Find :

• Area of quadrilateral

Let's do it ,

Area of the given quadrilateral

$\: \: \: \: \: \: \sf = Area \: of \: \triangle ABC + Area \: of \: \triangle DCB$

➠ Area of Triangle ABC = ½× 11 × 30

»» Area of Triangle ABC = 165 cm²

━━━━━━━━━━━━━━━━

➠ Area of Triangle DBC = ½× 19 × 30

»» Area of Triangle DBC = 285 cm²

So,

Area of quadrilateral will be = 165 + 185 = 450 cm²

Hence,

The area of quadrilateral is 450cm².

${\fcolorbox{red}{blue}{\orange{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: SugarCrash\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}$