The diagonal of a square is 10√2 cm. A new square is formed by joining midpoints of its sides. Find the area of the new square.
50 cm²
Let the side of the original square be \(s\). Since the diagonal \(= s\sqrt{2} = 10\sqrt{2}\), we get \(s = 10 \text{ cm}\).
Area of the original square \(= s^2 = 100 \text{ cm}^2\).
When the midpoints of the sides of a square are joined, the new square formed has exactly half the area of the original square.
So, the area of the new square \(= \frac{100}{2} = 50 \text{ cm}^2\).
Important Questions from Plane Figures
If length of a rectangle is increased to its three times and breadth is decreased to its half, then the ratio of the area of given rectangle to the area of new rectangle is:
The width of the path around a square field is 4.5 m and its area is 105.75 m 2. Find the cost of fencing the field at the rate of Rs. 100 per meter.
What is the area of the square (in cm 2) whose vertices lie on a circle of radius 5 cm?
The circumcentre of an equilateral triangle is at a distance of 3.2 cm from the base of the triangle. What is the length (in cm) of each of its altitudes?
The perimeter of a circular lawn is 1232 m. There is 7 m wide path around the lawn. The area (in m 2) of the path is:
Take \(\left(\pi=\frac{22}{7}\right)\)
