Question

Here is a rectangle of area 20 square cm. (a) Draw one straight line in this rectangle to divide it into two equal triangles. What is the area of each of the triangles?
(b) Draw one straight line in this rectangle to divide it into two equal rectangles. What is the area of each of the smaller rectangles?
(c) Draw two straight lines in this rectangle to divide it into one rectangle and two equal triangles.
• What is the area of the rectangle?
• What is the area of each of the triangles?

Answer 1

(a)
The given rectangle is divided into two equal triangles by drawing a line as shown below.



Area of rectangle = 20 square cm
Area of each triangle = $\frac{1}{2}$of area of rectangle
= (20 ÷ 2) square cm
= 10 square cm

(b)
The given rectangle is divided into two equal rectangles by drawing a line as shown below.



Area of rectangle = 20 square cm
Thus, area of each small rectangle = $\frac{1}{2}$of area of rectangle
= (20 ÷ 2) square cm
= 10 square cm

(c)
The given rectangle is divided into one rectangle and two equal triangles by drawing 2 lines as shown below.




We will consider a square as complete if it is more than half-filled, and will ignore a square if it is less than half-filled.

Thus, in the red shaded region, we have 2 completely filled squares and 2 squares that are more than half-filled.
Thus, the area of red triangle = 4 square cm

Similarly, the area of green triangle = 4 square cm
Now, the area of remaining portion i.e. the rectangle contains 12 completely filled squares.

• Thus, the area of rectangle = 12 square cm.
• Area of each of the triangle is 4 square cm.

Disclaimer: The answer to part (c) of the question may vary from student to student. The answer provided here is for reference only.