Question

how to find area of rhombus when parallel sides are 20 and 25 m and non parallel sides are 14 m and 13 m​

Answer 1

Correct question: Find the area of trapezium, whose parallel sides are 20 m and 25 m. And, non-parallel sides are 14m and 13m.

Answer:

292.5 m²

Step-by-step explanation:

[Refer to the attachment for the picture.]

Given that :

• The parallel sides are 20 m and 25 cm. And the non-parallel sides are 14m and 13 m.

Solution :

Draw DP || AB, such that ABPD forms a parallelogram. Here,

• BP = AD = 13 m
• AB = DP = 20 m
• PC = DC - DP = (25 - 20) = 5 m.

Now, in ΔBPC, sides are :

• a = 13 m
• b = 14 m
• c = 5 m

Semi perimeter, s = $\sf \dfrac{a + b + c}{2}$

⇒ s = $\sf \dfrac{13+ 14 + 5}{2}$

⇒ s = $\sf \dfrac{32}{2}$

⇒ s = 16 m

Area of ΔBPC = $\sf \sqrt{s(s-a)(s-b)(s-c)}$

= $\sf \sqrt{16(16 - 13)(16 - 14)(16 - 5)}$

= $\sf \sqrt{16 * 3 * 2 * 11}$

= $\sf \sqrt{1056}$

= 32.4961..

= 32.50 m² (approx.)

Also, area of ΔBPC = $\sf \dfrac{1}{2}$ * b * h

⇒ 32.5 = $\sf \dfrac{1}{2}$ * 5 * h

⇒ 65 = 5h

⇒ h = $\sf \dfrac{65}{5}$

⇒ h = 13 m

Now, find the area of parallelogram ABPD,

Area of ||gm ABPD = $\sf \dfrac{1}{2}$ * (AB + DP) * h

⇒ Area of ||gm = $\sf \dfrac{1}{2}$ * 40 * 13

⇒ Area of ||gm = 20 * 13

⇒ Area of ||gm = 260 m²

Total area of trapezium = Area of ΔBPC + Area of ||gm ABPD

⇒ Area of trapezium = ( 32.5 + 260 ) m²

⇒ Area of trapezium = 292.5 m²

Hence, the answer is 292.5 m².