Area and Perimeter Class 7

---

Class 7 Worksheet: Area and Perimeter (Advanced Level)

Section A: Multi-Step Problems

1. A rectangular field is 60 m long and 40 m wide.
   a) A path 5 m wide is built inside the field, running along its boundary. Find the area of the path.
   b) What is the remaining area of the field after constructing the path?

2. The perimeter of a rectangle is 200 m. Its length is 20 m more than its breadth.
   a) Find the dimensions of the rectangle.
   b) Calculate its area.

3. A trapezium has parallel sides measuring 18 cm and 12 cm, and the distance between the parallel sides is 10 cm.
   a) Find the area of the trapezium.
   b) If its non-parallel sides measure 8 cm each, calculate the perimeter.

4. A square and a rectangle have the same perimeter. The side of the square is 24 cm, and the rectangle's length is 30 cm.
   a) Find the breadth of the rectangle.
   b) Compare their areas.

---

Section B: Word Problems

5. A circular park has a diameter of 50 m.
   a) Calculate its area.
   b) A circular path 2 m wide is constructed around the park. Find the area of the path. (Take π = 3.14)

6. A floor is in the shape of a rectangle measuring 15 m × 10 m. Tiles of size 50 cm × 50 cm are used to cover the floor.
   a) How many tiles are needed to cover the floor?
   b) If one tile costs $12, find the total cost of the tiles.

7. The area of a triangle is 150 cm², and its base is 15 cm. Find:
   a) The height of the triangle.
   b) If the perimeter of the triangle is 50 cm, calculate the length of its other two sides (assume they are equal).

8. A piece of wire is 80 cm long and bent into the shape of a rectangle.
   a) If the length of the rectangle is twice its breadth, find the dimensions of the rectangle.
   b) Calculate its area.

---

Section C: Higher-Order Thinking Questions

9. A farmer has a square field with a side of 100 m. He wants to divide it into 4 smaller square plots of equal area and build a fence around each plot.
   a) Find the side of each smaller square plot.
   b) Calculate the total length of the fence required if the cost of fencing is $15 per meter.

A rectangular garden measuring 30 m × 20 m has a pond in the centre. The pond is in the shape of a circle with a radius of 7 m.
a) Find the area of the garden excluding the pond.
b) If grass is to be grown on the remaining area, calculate the cost at $8 per square meter. (Take π = 22/7)