You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VIII

Mathematics

Area of a General Quadrilateral

Area of a qua...

Question

Question 20

Area of a quadrilateral ABCD is $20 c m^{2}$ and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is
(a) 4 cm (b) 15 cm (c) 16 cm (d) 18 cm

Open in App

Solution

Area of the given quadrilateral $= \frac{1}{2}$ $\times$ (Sum of altitudes) $\times$ Corresponding diagonal
$\Rightarrow 20 = \frac{1}{2} (1 + 1.5) \times B D$ [given]
$\Rightarrow \frac{1}{2} \times 2.5 \times B D = 20 c m^{2}$
$\Rightarrow B D = 20 \times \frac{2}{2.5} = \frac{40}{2.5} = 16 c m$

Suggest Corrections

103

Similar questions

Area of a quadrilateral ABCD is $20 c m^{2}$ and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is

Q. Area of quadrilateral ABCD is 20

{c m}^{2}

and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is _______.

Question 20

Area of a quadrilateral ABCD is $20 c m^{2}$ and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is
(a) 4 cm (b) 15 cm (c) 16 cm (d) 18 cm

A B C D

is a quadrilateral in which diagonal

B D

is perpendicular to the side

A B

. If

A B = 4.5 c m

A D = 7.5 c m

and the distance of

C

from

B D

1.5 c m

, then find the area of quadrilateral.

Q. BD is one of the diagonals of a quadrilateral ABCD. AM and CN are the perpendiculars from A and C, respectively, on BD. Show that

a r (q u a d . A B C D) = \frac{1}{2} B D . (A M + C N)

Join BYJU'S Learning Program

Explore more

Area of a General Quadrilateral

Standard VIII Mathematics

Join BYJU'S Learning Program

Question 20 Area of a quadrilateral ABCD is 20 cm2 and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is (a) 4 cm (b) 15 cm (c) 16 cm (d) 18 cm

Area of the given quadrilateral =12 × (Sum of altitudes) × Corresponding diagonal ⇒20=12(1+1.5)×BD [given] ⇒12×2.5×BD=20cm2 ⇒BD=20×22.5=402.5=16 cm

Question 20

Area of a quadrilateral ABCD is $20 c m^{2}$ and perpendiculars on BD from opposite vertices are 1 cm and 1.5 cm. The length of BD is
(a) 4 cm (b) 15 cm (c) 16 cm (d) 18 cm

Area of the given quadrilateral $= \frac{1}{2}$ $\times$ (Sum of altitudes) $\times$ Corresponding diagonal
$\Rightarrow 20 = \frac{1}{2} (1 + 1.5) \times B D$ [given]
$\Rightarrow \frac{1}{2} \times 2.5 \times B D = 20 c m^{2}$
$\Rightarrow B D = 20 \times \frac{2}{2.5} = \frac{40}{2.5} = 16 c m$