In the given figure, AC is a diagonal of quad. ABCD in which BL ⊥ AC and DM ⊥ AC. Prove that or (quad. ABCD) $= \frac{1}{2} \times A C \times (B L + D M)$ .]

Open in App

Solution

AC is one of the diagonal of quadrilateral ABCD. Also, BL ⊥ AC and DM ⊥ AC.
Then area of ABCD = ar(∆ADC) + ar(∆ABC)
Now, ar(∆ADC) = $\frac{1}{2}$ ⨯ AC ⨯ BL (BL ⊥ AC)
Also, ar(∆ABC) = $\frac{1}{2}$ ⨯ AC ⨯ DM (DM ⊥ AC)
∴ Area of ABCD = ( $\frac{1}{2}$ ⨯ AC ⨯ BL) + ( $\frac{1}{2}$ ⨯ AC ⨯ DM)
= $\frac{1}{2}$ ⨯ AC ⨯ (BL + DM)

Suggest Corrections

Similar questions

In the given figure, $A B C D$ is a quadrilateral in which $A C = 24 c m, B L ⊥ A C$ and $D M ⊥ A C$ such that $B L = 8 c m$ and $D M = 7 c m .$ Find the area of quadrilateral $A B C D .$

Q. find the area of pentagon

A B C D E A

in which

B L ⊥ A C, D M ⊥ A C

and

E N ⊥ A C

such that AC=18cm, AM= 14 cm, AN = 6 cm, BL = 4 Cm , DM =12 cm and EN=9 cm

Find the area of pentagon ABCDE in which $B L ⊥ A C,$ $D M ⊥ A C$ and $E N ⊥ A C$ such that $A C = 18 c m,$ $A M = 14 c m,$ $A N = 6 c m,$ $B L = 4 c m,$ $D M = 12 c m$ and $E N = 9 c m .$