Area

[Śulba-Sūtras] Give a method to transform a rectangle into a triangle of equal area.

[Śulba-Sūtras] Give a method to transform a triangle into a rectangle of equal area.

What measurements would you need to find the area of a regular hexagon?

Give a method to obtain a quadrilateral whose area is half that of a given quadrilateral.

Consider a rectangle and a parallelogram of the same sidelengths: 5 cm and 4 cm. Which has the greater area?

Give a method to obtain a rectangle whose area is twice that of a given triangle. What are the different methods that you can think of?

[Śulba-Sūtras] Give a method to obtain a rectangle of the same area as a given triangle.

[Śulba-Sūtras] An isosceles triangle can be converted into a rectangle by dissection in a simpler way. Can you find out how to do it?

[Śulba-Sūtras] Give a method to convert a rectangle into an isosceles triangle by dissection.

Which has greater area—an equilateral triangle or a square of the same sidelength as the triangle? Which has greater area—two identical equilateral triangles together or a square of the same sidelength as the triangle? Give reasons.

Find the area of a rhombus whose diagonals are 20 cm and 15 cm.

Give a method to convert a rectangle into a rhombus of equal area using dissection.

[Śulba-Sūtras] Give a method to convert an isosceles trapezium to a rectangle using dissection.

Using the idea of converting a trapezium into a rectangle of equal area, and vice versa, construct a trapezium of area 144 cm².