Question

.All sides of a Parallelogram are of length 10cm and one of its diagonals is of length 16 cm.

a) What is the length of the other diagonal?
b) Find the area of the Parallelogram.​

Answer 1

Solution :-

we know that,

• when all sides of a parallelogram are equal it will be a rhombus .
• Diagonals of a rhombus bisect each other at 90° .

so,

→ CI = IA = 16 / 2 = 8 cm.

now, in right ∆BIA ,

→ IA = 8 cm .

→ AB = 10 cm. (given)

then,

→ BI = √(AB² - IA)² (by pythagoras theorem)

→ BI = √(10² - 8²)

→ BI = √(100 - 64)

→ BI = √36 = 6 cm.

so,

→ BD = 2 * BI = 2 * 6 = 12 cm. (Ans.)

therefore,

→ Area of the parallelogram = (1/2) * Diagonal 1 * Diagonal 2 = (1/2) * 12 * 16 = 96 cm². (Ans.)

Learn more :-

In ABC, AD is angle bisector,

angle BAC = 111 and AB+BD=AC find the value of angle ACB=?

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