Question

Find the area of a parallelogram ABCD in which:
AB = 14 cm, BC = 10 cm and AC = 16 cm.
[Use 3 = 1.73]​

Answer 1

Answer:

Refers to the attachment for the Answer.

From the attachment.

In Δ ABC,

Using Heron's Formula,

S = (a + b + c)/2

⇒ S = (10 + 14 +16)/2

⇒ S = 40/2

⇒ S = 20

Area =

∴ Area of the triangles =

⇒ Area of Δ ABC =

⇒ Area = √4800

⇒ Area = 10√48

⇒ Area = 10√(2 × 2 × 2 × 2 × 3)

⇒ Area = 10 × 2 × 2√3

⇒ Area of Δ ABC = 40√3 cm²

∴ Area of Δ ABC = 69.28 cm².

We know,

Area of the Δ ADC = Area of the ΔABC.

[∵ Both the triangles are congruent)

∴ Area of the Parallelogram = 2 × Area of Δ ABC.

⇒ Area of the Parallelogram = 2 × 69.28 cm²

∴ Area of the Parallelogram = 138.56 cm².

Hence, the Area of the Parallelogram is 138.56 cm².

[ Note ⇒ The answer is different in points because I have taken the Exact value of √3. Although, it does not effect, such errors should be neglected.]

Hope it helps.