The figure above shows a parallelogram $A B C D$ with $A C = 3$ and $A D = 5$ . Calculate the area of parallelogram $A B C D$ .

12

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

15

No worries! We‘ve got your back. Try BYJU‘S free classes today!

18

No worries! We‘ve got your back. Try BYJU‘S free classes today!

20

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $12$
$Δ A B C$ is congruent to $Δ A D C$ , with angles $∠ B A C$ and $∠ A C D$ being of measure $90^{o}$
$∴ (C D)^{2} + (A C)^{2} = (A D)^{2}$
$∴ 9 + (C D)^{2} = 25$
$∴ C D = 4$
Area of $Δ A C D = \frac{1}{2} \times A C \times C D$
$= \frac{1}{2} \times 3 \times 4$
$= 6$ , which is also the area of $Δ A B C$
$∴$ area of parallelogram $A B C D = 12$

Suggest Corrections

Similar questions

The given figure shows parallelogram ABCD. Points P and Q trisect the side AB, then which of the following is correct?

Q. The following figure shows two parallelograms ABCD and ABEF, If the area of the parallelogram ABCD is

70 c m^{2}

; then find the area of the parallelogram ABEF

Q. In a parallelogram

A B C D, A B = 16 c m, B C = 12 c m

and diagonal

A C = 20 c m

. Find the area of the parallelogram.

Q. In the adjoining figure, show that ABCD is a parallelogram.
Calculate the area of || gm ABCD.

The given figure shows parallelogram ABCD. Points P and Q trisects the side AB.
To prove: Area of $△$ DPQ = $\frac{1}{6}$ × Area of (parallelogram ABCD)

Join BYJU'S Learning Program

The figure above shows a parallelogram ABCD with AC=3 and AD=5. Calculate the area of parallelogram ABCD.

The correct option is A 12ΔABC is congruent to ΔADC, with angles ∠BAC and ∠ACD being of measure 90o∴(CD)2+(AC)2=(AD)2∴9+(CD)2=25∴CD=4Area of ΔACD=12×AC×CD=12×3×4=6, which is also the area of ΔABC∴ area of parallelogram ABCD=12

The figure above shows a parallelogram $A B C D$ with $A C = 3$ and $A D = 5$ . Calculate the area of parallelogram $A B C D$ .