two adjacent sides of a parallelogram are 74cm and 40 cm and one of its diagonals is 102.Area of the parallelogram
Answers
Answer:
Consider AB=51cm, BC=37cm and AC=20cm.
In ΔABC,
s=
2
a+b+c
=
2
51+37+20
=54
The area of ΔABC is,
A=
s(s−a)(s−b)(s−c)
=
54(54−51)(54−37)(54−20)
=
54(3)(17)(34)
=
93636
=306cm
2
The area of parallelogram is the twice of ΔABC,
A=2×306
A=612cm
2
Answer:
Given,
Two adjacent side of Parallelogram are 74 cm and 40 cm.
• One of parallelogram diagonal is 102 cm
To Find :
• Area of Parallelogram = ?
Find :
Suppose the two adjacent side of parallelogram be a and b side of traingle.
Suppose the length of diagonal be c side of traingle
Therefore,
→ These two sides and one diagonal divide the parallelogram into two triangle.
Now Find Triangle Area :
⇒.. Semi S= Perimeter = 74+40+102 2 a+b+c 2
216 S= = 108 cm
Now Using Heron's Formula to Find Area of triangle :
:⇒ √s(s-a)(s — b)(s — c)
/108(108 – 74) (108 – 40) (108 - 10
: √108 x 34 x 68 x 6
: 6 × 2 × 3 × 34
:→ 1224 cm²
Now Find Area of Parallelogram :
→ Area of Parallelogram = 2 x Area of Triangle
→ 2 x 1224
→ 2448 cm ²
Hope it helps you
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