Area and volume using formulae worksheet

This worksheet, aimed at Key Stage 2 students, is designed to enhance their understanding of geometric relationships and the use of formulae in calculating area and volume. The core objective is for students to recognise that shapes with identical areas can have different perimeters and vice versa. Additionally, the worksheet encourages students to identify when it is appropriate to apply formulae to determine the area and volume of various shapes.

The first activity requires squared paper and rulers, with students being tasked to draw a shape of a specific area and then alter it to have the same area but different perimeters, illustrating the concept that area and perimeter are independent properties. A variation of this activity flips the challenge, asking students to maintain a constant perimeter while varying the area. The second activity continues the exploration of this concept with rectangles, presenting examples where the perimeter is less than the area, and prompting students to consider if the opposite can be true. Finally, the third activity engages students in formulating mathematical expressions to calculate the perimeter and area of given shapes, reinforcing their understanding of geometric formulae and their practical application.