Question

A side of rohmbus PQRS measures 8.5 units. if the length of the diagonal QS is 8 units, find the area of a rhombus.​

Answer 1

Answer:

• 60 sq• unit

Given:-

• A side of Rhombus PQRS measures 8.5 units
• The length of diagonal QS is 8 units

To Find :-

• The area of rhombus

Diagram:-

• Refer to the attachment

Step-by-step explanation:

We know, the formula of area of rhombus is,

$\boxed{ \sf{A_{rhombus} = \frac{p \times q}{2} }}$

where,

• p and q are two diagonal of rhombus.

So, to find the area, first we need to find two diagonals.

Now, we know the two diagonals of a rhombus bisects each other with the angle of 90°

And let the intersection point be O

Therefore, POQ is a right angle triangle

PQ = 8.5 unit (Side of a rhombus)

OQ = 8 ÷ 2 = 4 unit

Now, Hypotenuse PO would be,

$\implies \sf \: PO = \sqrt{ {PQ} ^{2} - {QO}^{2} }$

$\implies \sf \: PO = \sqrt{ {8.5} ^{2} - {4}^{2} }$

$\implies \sf \: PO = \sqrt{ 72.25 - 16}$

$\implies \sf \: PO = \sqrt{ 56.25}$

$\implies \sf \: PO = 7.5$

Now, the length of diagonal is

$\implies \sf \: PR = 7.5 \times 2 = 15 \: unit$

Now, the area of rhombus is,

$\boxed{ \sf{A_{rhombus} = \frac{8 \times 15}{2} }}$

$\implies \sf \: 4 \times 15 = 60 \: sq.unit$

Answer 2

Answer:

side of rohmbus PQRS measures 8.5 units. if the length of the diagonal QS is 8 units, find the area of a rhombus.​

Step-by-step explanation: