2024 · Q48
A square is drawn inside a square of side 14 cm in such a way that the corners of the inner square coincide with the mid points of the sides of the outer square. What is the area lying between the two squares?
Elementary MathematicsQuadrilaterals and Polygons
- A98 square cm
- B56 square cm
- C49 square cm
- D24.5 square cm
Explanation
Joining the mid-points of the outer square's sides forms the inner square with side √(7²+7²) = 7√2 cm (each side is the hypotenuse of a 7-7 right triangle). Its area is (7√2)² = 98 sq cm. The outer square has area 14² = 196 sq cm, so the region between them is 196 − 98 = 98 sq cm — option A.