Question

Calculate the area of the square JKLM if KM = 42 mm.

Answer 1

Calculate the area of the square JKLM if KM = 42 mm.

given that KM=42 mm

KM is also the diagonal of the square.

Also, the diagonal KM is the hypotenuse of a right triangle with sides JK and JM the Pythagoras theorem.

Now , let's remember that the angle formed by two sides of a square is equal to 90 degrees, this means, that the angle formed by the diagonal and any side must be the half, it is 45 degrees

so, if we solve the right triangle MLK we will find the length of the s

`\begin{gathered} \text{cos}\emptyset=\frac{x}{\text{Hypotenuse}} \\ x=\text{Hypotenuse }\cdot\text{ cos}\emptyset \\ x=42\cdot\cos 45 \\ x=29.69 \end{gathered}`

Now, is it a square, so the sides are equal, and the area is given by

`\begin{gathered} \text{Area}=x^2 \\ A\text{rea}=(29.698)^2 \\ \text{Area}=882\text{ square milimeteres} \end{gathered}`

so, the answer is 882 square millimeters