Construction of Plane Figures

Construction of Triangle and Rectangle of Equal Areas:

Steps:

i. Draw the given triangle ABC and its perpendicular height CY.

ii. Construct the perpendicular bisector of CY as X.

iii. From points A and B, draw a perpendicular to meet the bisector of CY at P and Q.

iv. ABQP is the required rectangle which is of equal area to the triangle.

Construction of Square and a Rectangle of Equal Areas:

i. Draw the given rectangle ABCD

ii. Extend side AB. Draw an arc centred at B with radius BC.

iii. Let E be the intersection of the arc and ray AB.

iv. Construct the midpoint F of segment AE by bisecting the AE.

v. Construct a circle centred at F with radius FA.

vi. Extend side CB. Let G be the point where the circle and ray CB intersect.

vii. Then BG is the side of the desired square.

viii. Complete by constructing a square with side BG.

The area of the Rectangle ABCD is the same as the area of Square BGHI.

Technical Drawing Questions:

Using a ruler and a pair of compasses only, construct a square with side AB = 80 mm.