Question

help me answer this question.

The midpoint of the diagonal of a square is 2 units from the vertex of the square. Calculate the area of the square

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Answer 1

Answer:

8 units²

Step-by-step explanation:

Let side of the square = a

The , Area of square = a²

Now, Midpoint of Diagonal DB is E

And DE = 2 units

So, DB = 2 DE = 2 × 2 = 4 units

Now, using Pythagoras theorem in ∆ BCD

DB² = DC² + BC²

plug the values

${4}^{2} = {a}^{2} + {a}^{2}$

Collect like terms

${4}^{2} = 2 {a}^{2}$

Evaluate the power

$16 = 2 {a}^{2}$

Swipe the side of the equation

$2 {a}^{2} = 16$

Divide both sides of the equation by 2

$\frac{2 {a}^{2} }{ 2 } = \frac{16}{2}$

Calculate

${a}^{2} = 8$

Therefore, The area of the square is 8 sq.units.

Hope this helps..

Best regards!!

Answer 2

Answer:

8 units²

This was the answer.