AreaClass 8 Mathematics Case Study Questions

A rectangular public park has a length of $100$ m and a breadth of $70$ m. A pathway of uniform width $5$ m is constructed all around the inside of the park. The park management decides to plant grass on the remaining portion of the park, which forms an inner rectangle. The pathway is to be paved with red bricks. The cost of planting grass is ₹45 per square metre, and the cost of paving the pathway with bricks is ₹110 per square metre. The management needs to calculate the costs for budgeting purposes.

For a kite festival, Priya decides to make a kite in the shape of a rhombus. The kite's paper is made from a single rhombus shape whose diagonals measure $d_1 = 48$ cm and $d_2 = 32$ cm. To make the design interesting, the rhombus is divided into four triangles by its diagonals. She colours two opposite triangles with green paper and the other two opposite triangles with yellow paper. The cost of green paper is ₹0.20 per cm² and yellow paper is ₹0.15 per cm². She also adds a tail to the kite, which is an isosceles triangle with a base of $10$ cm and a height of $20$ cm, made from yellow paper.

A rectangular community garden is $80$ m long and $60$ m wide. Two cross-paths are built in the exact center of the garden, running parallel to its sides. The path parallel to the length is $2$ m wide, and the path parallel to the breadth is $3$ m wide. The remaining four rectangular plots are used for planting flowers. The cost of laying the paths is ₹120 per square metre, and the cost of preparing the soil for the flower plots is ₹30 per square metre.