Given,
The two adjacent sides of a parallelogram = 10 cm and 12 cm
One of the diagonals = 8 cm
To find,
The area of the parallelogram.
Solution,
The area of the parallelogram will be 30√7 cm².
We can easily solve this problem by following the given steps.
According to the question,
The two adjacent sides of a parallelogram = 10 cm and 12 cm
One of the diagonals = 8 cm
Let's take ABCD as a parallelogram.
AB (a) = 12 cm
BC (b) = 10 cm
AC (c) = 8 cm
Now, ABC is a triangle of the same area as triangle ADC.
We know that the area of a triangle can be found using Heron's formula:
Semi- perimeter (s) = (a+b+c)/2
's' = (12+10+8)/2
's' = 30/2 cm
's' = 15 cm
Now, using Heron's formula:
A = [tex] \sqrt{s(s - a)(s - b)(s - c)} [/tex]
A = [tex] \sqrt{15(15 - 12)(15 - 10)(15 - 8)} [/tex]
A = [tex] \sqrt{15(3)(5)(7)} [/tex]
A = [tex] \sqrt{45 \times 35} [/tex]
A = [tex] \sqrt{1575} [/tex]
A = [tex]15 \sqrt{7} [/tex] cm²
Now,
Area of parallelogram = Area of ∆ ABC + Area of ∆ ADC
Area = (15√7 + 15√7) cm²
Area = 30√7 cm²
Hence, the area of the parallelogram is 30√7 cm².
