Maths ·Class 9 Maths

Since ∆ABD and ∆ACD have equal area, you may wonder - Can we divide ∆ABD using straight cuts Class 9

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· Jul 14, 2026 · Reviewed & updated Sep 17, 2026 · 2 min read

Since ∆ABD and ∆ACD have equal area, you may wonder - Can we divide ∆ABD using straight cuts Class 9

Question 1.

Since ∆ABD and ∆ACD have equal area, you may wonder - Can we divide ∆ABD using straight cuts into two or more pieces that we can then rearrange to exactly cover ∆ACD? What do you think? Is it possible? Class 9

Answer:

Yes, it is possible.

Since ∆ABD and ∆ACD have equal area, one triangle can be cut into a finite number of pieces and rearranged to exactly cover the other triangle.

In fact, ∆ABD can be divided into a small number of parts (using straight cuts), and these parts can be rearranged without overlap or gaps to exactly cover ∆ACD.

Question 2.

Suppose we are given two polygons P and Q with equal area. Will it always be possible to divide one of them using straight cuts into two or more pieces and then rearrange the pieces to exactly cover the other polygon? Try this out for familiar shapes, e.g., Class 9

i. A square and non-square rectangle with equal area,

ii. Two triangles with different shapes but equal area,

iii. A triangle and a square with equal area. Formulate a conjecture of your own about this.

Answer:

Yes, it is always possible. Any two polygons with equal area can be divided into pieces using straight cuts and rearranged to exactly cover each other.

i. A square and a non-square rectangle with equal area:

Draw a square of side 4 cm and a rectangle of 2 cm × 8 cm — both have area 16 cm². Now make a few straight cuts in the rectangle. You will find that the pieces can be shifted and rearranged to perfectly fit the square.

ii. Two triangles with different shapes but equal area:

Draw two triangles, both with base 6 cm and height 4 cm but different types. Both have area 12 cm². Even though they look different, cutting one into a few pieces and rearranging them will exactly cover the other.

iii. A triangle and a square with equal area: Draw a triangle with base 8 cm and height 4 cm, and a square of side 4 cm, both have area 16 cm². Making straight cuts in the triangle gives pieces that fit together perfectly to form the square.

Conjecture: If two polygons have equal area, one can be divided into a finite number of pieces using straight cuts and rearranged to exactly cover the other, regardless of their shapes.