QuadrilateralsClass 8 Mathematics Case Study Questions

A local community is designing a new garden with several plots for growing vegetables and herbs. An architect has proposed a design where the main vegetable plot, named ABCD, is a parallelogram. The adjacent sides AB and AD are planned to be $6$ meters and $4$ meters respectively, with the angle between them, $\angle DAB$, being $60^{\circ}$. Next to it, a rectangular herb garden, PQRS, is planned. To maintain a sense of uniformity, the architect wants the perimeter of the rectangular herb garden to be the same as the perimeter of the parallelogram plot. The community members need to calculate various dimensions and angles to buy the right amount of fencing and to position the plots correctly. They will use the properties of quadrilaterals to finalize their plan.

For a school festival, a workshop on kite making is organized. A student, Rohan, decides to build a kite using two wooden sticks as its diagonals. He has one stick of length $80$ cm and another of length $60$ cm. Following the traditional design of a kite, he arranges the sticks to be perpendicular to each other. The longer stick forms the main spine of the kite. He ensures that the shorter stick is bisected by the longer one. The intersection point divides the longer stick into two parts, one of length $30$ cm and the other of length $50$ cm. Now, he needs to connect the endpoints of the sticks with thread to form the outer frame of the kite. Rohan uses his knowledge of quadrilaterals to determine the lengths of the thread needed for each side.

An interior designer is planning to tile the floor of a large hall using identical rhombus-shaped tiles. Each tile has all its sides equal to $50$ cm. The designer specifies that one of the angles of the rhombus must be $120^{\circ}$. The tiles need to be laid adjacent to each other to cover the entire floor. To calculate the number of tiles needed and to ensure they fit perfectly, the designer's assistant needs to understand the geometric properties of these rhombus tiles, such as their other angles and the properties of their diagonals. The assistant recalls that a rhombus is a special type of parallelogram and uses this fact to deduce other measurements.