Worksheet Chapter 10: Perimeter and Area

1. True or False: Among all rectangles with a fixed perimeter, a square has the maximum area.

2. A kite has an area of 48 cm². If one of its diagonals measures 12 cm, find the length of the other diagonal.

3. Calculate the area of a trapezium with parallel sides measuring 7 cm and 11 cm, and a perpendicular distance of 6 cm between them.

4. True or False: The area of a parallelogram with base 10 cm and height 5 cm is equal to the area of a triangle with base 10 cm and height 5 cm.

5. A wire of length 60 cm is bent to form a rectangle. (a) State the dimensions of the rectangle that yields the maximum area. (b) Calculate that maximum area.

6. A rectangular garden measures 15 m long and 8 m wide. A path of uniform width 1 m is built around the outside of the garden. Calculate the outer perimeter of the path.

7. A composite shape is made up of a square ABCD with side 8 cm and an isosceles triangle BCE attached to side BC. If the total perimeter of the composite shape is 40 cm, find the length of one of the equal sides of the triangle.

8. A room floor measuring 6 m by 4 m needs to be tiled with square tiles of side 20 cm. Calculate the minimum number of tiles required to cover the floor.

9. The ratio of the length to the width of a rectangle is 3 : 2. If the perimeter of the rectangle is 50 cm, calculate its area.

10. Fill in the blank: The total length around the boundary of a closed 2D shape is called its ________.