Question

find the area of parallelogram in which ab =14cm ,bc=10cm and ac= 26cm

Answer 1

The area of parallelogram is 140cm

Answer 2

See 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.

Hope it helps.
Thanks.