Question

Find the area of the parallalogram whosd adjacent sides are 60cm and 40cm and a diagonal is 80cm long​

Answer 1

Answer:

Area of the parallelogram is 2322 cm² .

Step-by-step explanation:

Given :

• Adjacent sides of parallelogram are 60 cm and 40 cm.
• And one diagonal measure is 80 cm.

To find :

• Area of the parallelogram.

Solution :

Suppose, ABCD is a parallelogram and ACD is triangle. AO is height of parallelogram and triangle. Base of triangle and base of parallelogram is DC. Base of parallelogram and triangle are same.

• For area of parallelogram first we need height of parallelogram. Height of parallelogram and triangle are same. So,

Finding length of AO :

In ∆ACD :

Using Heron's formula :

• Area of triangle = √[s(s - a)(s - b)(s - c)]

[Where, a, b and c are sides and s is semi-perimeter of triangle]

So,

$\implies$ s = Perimeter of triangle/2

• DC = 60 cm
• AD = 40 cm
• AC = 80 cm

$\implies$ s = (60 + 40 + 80)/2

$\implies$ s = 180/2

$\implies$ s = 90

Semi-perimeter is 90 cm.

Area of triangle :

$\implies$ √[90(90 - 60)(90 - 40)(90 - 80)]

$\implies$ √[90 × 30 × 50 × 10]

$\implies$ √[2 × 3 × 3 × 5 × 2 × 3 × 5 × 2 × 5 × 5 × 2 × 5]

$\implies$ 2 × 2 × 3 × 5 × 5 × √(5 × 3)

$\implies$ 300√15

• √15 = 3.87

$\implies$ 300 × 3.87

$\implies$ 1161

Area of triangle ACD is 1161 cm².

For height :

• Area of triangle = ½ × base × height

$\implies$ 1161 = 1/2 × AO

$\implies$ 1161 = 1/2 × 60 × AO

$\implies$ (1161 × 2)/60 = height

$\implies$ 2322/60 = AO

$\implies$ AO = 38.7

Length of AO is 38.7 cm.

• Height of parallelogram and triangle are same.

Thus,

Height (AO) of parallelogram is 38.7 cm

Now,

• Area of parallelogram (ABCD) = base × height

• Base = DC = 60 cm.
• Height = AO = 38.7 cm

$\implies$ Area = 60 × 38.7

$\implies$ Area = 2322

Therefore,

Area of the parallelogram is 2322 cm².