CBSE Class 5 Mathematics How Many Squares Worksheet Set 03

Question 1. Is the area of both the figures same? Give reasons for your answer.
Answer: Yes, the area of both figures is the same.
Reason: The first figure is a triangle formed by cutting a rectangle/square grid diagonally in half. The second figure is a full square region on the same grid. If we count the number of unit squares: the first figure occupies exactly half of a 4 \(\times\) 4 grid area (which equals 8 unit squares), or more simply, a square of size 3 \(\times\) 3 or similar grid units can be compared by counting full and half squares. Specifically, looking at the grid, the triangle covers 8 full or equivalent half-squares, and the square on the right also covers 8 square units. Thus, both figures have an equal area of 8 square units.
In simple words: Both shapes cover the exact same number of grid squares, so their areas are equal.
Exam Tip: Always count the total number of full squares and half squares inside a grid region to find and compare areas accurately.

Question 2. What is the area of the shaded part?
Answer: Let us analyze the two diagrams given in Question 2:
1. In the first diagram, a rectangle consisting of 2 equal squares is shown, where exactly one square is shaded with cross-hatch lines. If each grid square is 1 unit by 1 unit, the shaded part covers 1 full square region, so its area is 4 square units (assuming each grid block is 2 \(\times\) 2) or 1 unit depending on standard grid scale. Looking closely at the grid lines, the rectangle has a width of 4 units and height of 2 units (total 8 squares), and half of it (the right square box) is shaded, giving an area of 4 square units.
2. In the second diagram, a square region is divided diagonally by a line, and the upper-left triangle is shaded. Since the diagonal divides the square into two equal halves, the area of the shaded triangle is exactly half of the total area of the square. If the square is 3 \(\times\) 3 (9 square units) or 4 \(\times\) 4 (16 square units), the shaded triangle represents half of that total area.
In simple words: The shaded part in each figure represents exactly half of the total grid area shown.

Exam Tip: When shapes are symmetrical or divided by a diagonal line, the area of one half is simply \(\frac{1}{2}\) of the total area of the figure.

Please refer to attached file for CBSE Class 5 Maths Worksheet-How Many Squares (3)