Practical Geometry

Step 1 – Draw a Line BE of length 5 cm

Step 2 – Draw a circle of Radius 8 cm centered at B.

Step 3 – Draw a circle of radius 5 cm centered at E.

The intersection point of the two circle gives the point S.

Step 4 – Draw lines BT and ST parallel to ES and EB respectively both of length 5 cm.

Measure the lengths of its Diagonals D₁ and D₂ and then find the area by

Area =

Step 1 – Draw a line BE of length 6 cm.

Step 2 – Draw a circle of radius 8.2 cm Centered at E and a circle of radius 6 cm centered at B.

Step 3 – Complete the Rhombus by making ES and ST parallel to BT and EB respectively of length 6 cm each.

Measure the lengths of its Diagonals D₁ and D₂ and then find the area by

Area =

Step 1 – Draw a line BE of length 6 cm.

Step 2 – Draw a line at an angle 45° from point B and make a circle of radius 6 cm centered at E, the point of intersection of this line and this circle gives us the point S.

Step 4 – Complete the Rhombus by making BT and ST parallel to SE and BE.

Measure the lengths of its Diagonals D₁ and D₂ and then find the area by

Area =

Step 1 – Draw a line BE of length 7.5 cm.

Step 2 – Draw a line at an angle 65° from E and circle of radius 7.5 cm centered at E, the intersection of this line and circle gives the point S.

Step 4 – Complete the Rhombus by making BT and ST parallel to BE and SE respectively.

Measure the lengths of its Diagonals D₁ and D₂ and then find the area by

Area =

Diagonals of a Rhombus bisect each other at Right Angle.

Step 1 – Draw a line BS of length 10 cm and a line ET of length 8 cm which is a perpendicular bisector of line BS.

Step 2 – Join the four points to make the Rhombus.

Measure the lengths of its Diagonals D₁ and D₂ and then find the area by

Area =

Diagonals of a Rhombus bisect each other at Right Angle.

Step 1 – Draw a line BS of length 10 cm and a line ET of length 8 cm which is a perpendicular bisector of line BS.

Step 2 – Join the four points to make the Rhombus.

BS is a diagonal

Step 1 – Draw a line BS of length 10 cm.

BS is an angle bisector of ∠B as it is a diagonal in the Rhombus.

Also, opposite angles of a Rhombus are equal.

Step 2 – Draw lines at an angle 30° from B and S.

Here, ∠B = ∠S = 60°

∴ they make 30° with the diagonal BS as it is an angle bisector in a Rhombus.

Step 3 – Mark the intersecting points as E and T to complete the Rhombus.

Measure the lengths of its Diagonals D₁ and D₂ and then find the area by

Area =

ET is a diagonal

Step 1 – Draw a line ET of length 9 cm.

ET is an angle bisector of ∠E as it is a diagonal in the Rhombus.

Also, opposite angles of a Rhombus are equal.

Step 2 – Draw lines at an angle 35° from E and T.

Here, ∠E = ∠T = 70°

∴ they make 35° with the diagonal ET as it is an angle bisector in a Rhombus.

Step 3 – Mark the intersecting points as B and S to complete the Rhombus.

Measure the lengths of its Diagonals D₁ and D₂ and then find the area by

Area =

Step 1 – Construct a line JU of length 5.4 cm

Step 2 – Construct a line UM of length 4.7 cm perpendicular to the line JU.

Step 3 – Complete the rectangle by making JP and PM perpendicular to JU and UM respectively.

Area = length × breadth

A = 5.4 × 4.7

A = 25.38 cm²

Step 1 – Construct a line JU of length 6 cm

Step 2 – Construct a line JP of length 5 cm perpendicular to the line JU.

Step 3 – Complete the rectangle by making UM and PM perpendicular to JU and JP respectively.

Area = length × breadth

A = 5 × 6

A = 30 cm²

Step 1 – Construct a line JP of length 4.2 cm

Step 2 – Construct a line MP of length 2.8 cm perpendicular to the line JP.

Step 3 – Complete the rectangle by making JU and MU perpendicular to JP and MP respectively.

Area = length × breadth

A = 2.8 × 4.2

A = 11.76 cm²

Step 1 – Construct a line MP of length 4.6 cm

Step 2 – Construct a line UM of length 3.6 cm perpendicular to the line MP.

Step 3 – Complete the rectangle by making JP and UJ perpendicular to MP and UM respectively.

Area = length × breadth

A = 3.6 × 4.6

A = 16.56 cm²

Step 1 – Construct a line MO = 5 cm

Step 2 – Draw a ray perpendicular to MO passing through O

Step 3 – Cut an arc of length 6.5 cm on the ray with M as center and mark the intersecting point as R.

Step 4 – Complete the rectangle by making RO and MO perpendicular to RE and ME respectively.

Measure RE

⇒ RE = 4.2 cm

Area = 5 × 4.2

Area = 21

Step 1 – Construct a line MO = 4.6 cm

Step 2 – Draw a ray perpendicular to MO passing through M

Step 3 – Cut an arc of length 5.4 cm on the ray with O as center and mark the intersecting point as E.

Step 4 – Complete the rectangle RE and EO perpendicular to MR and MO respectively.

Measure OE

⇒ OE = 2.8 cm

Area = 4.6 × 2.8

Area = 12.88 cm²

Step 1 – Construct a line OR = 3 cm

Step 2 – Draw a ray perpendicular to OR passing through O

Step 3 – Cut an arc of length 5 cm on the ray with R as center and mark the intersecting point as M.

Step 4 – Complete the rectangle ME and RE perpendicular to MO and OR respectively.

Measure RE

⇒ RE = 4 cm

Area = 3 × 4

Area = 12 cm²

Step 1 – Construct a line OR = 3 cm

Step 2 – Draw a ray perpendicular to ME passing through M

Step 3 – Cut an arc of length 6 cm on the ray with E as center and mark the intersecting point as O.

Step 4 – Complete the rectangle OR and RE perpendicular to MO and ME respectively.

Measure RE

⇒ RE = 5.2 cm

Area = 3 × 5.2

Area = 15.6 cm²

Step 1 – Construct a line EA of length 5.1 cm.

Step 2 – Draw lines AS and EY perpendicular to EA of length of EA.

Step 3 – Join S and Y

Area of Square = side × side = side²

Area = 5.1² = 26.01 cm²

Step 1 – Construct a line EA of length 3.8 cm.

Step 2 – Draw lines AS and EY perpendicular to EA of length of EA.

Step 3 – Join S and Y

Area of Square = side × side = side²

Area = 3.8² = 14.44 cm²

Step 1 – Construct a line EA of length 6 cm.

Step 2 – Draw lines AS and EY perpendicular to EA of length of EA.

Step 3 – Join S and Y

Area of Square = side × side = side²

Area = 6² = 36 cm²

Step 1 – Construct a line EA of length 4.5 cm.

Step 2 – Draw lines AS and EY perpendicular to EA of length of EA.

Step 3 – Join S and Y

Area of Square = side × side = side²

Area = 4.5² = 20.25 cm²

Step 1 – Draw a line GL of length 4.8 cm

Step 2 – Draw a perpendicular bisector DO of GL of same length as GL

HERE GL = DO = 4.8 cm

Step 3 – Join the four points GOLD

Area of square = (where D is the Diagonal)

Area =

Area = 11.52 cm²

Step 1 – Draw a line GL of length 3.7 cm

Step 2 – Draw a perpendicular bisector DO of GL of same length as GL

HERE GL = DO = 3.7 cm

Step 3 – Join the four points GOLD

Area of square = (where D is the Diagonal)

Area =

Area = 6.845 cm²

Step 1 – Draw a line GL of length 5 cm

Step 2 – Draw a perpendicular bisector DO of GL of same length as GL

HERE GL = DO = 5 cm

Step 3 – Join the four points GOLD

Area of square = (where D is the Diagonal)

Area =

Area = 12.5 cm²

Step 1 – Draw a line GL of length 7 cm

Step 2 – Draw a perpendicular bisector DO of GL of same length as GL

HERE GL = DO = 7 cm

Step 3 – Join the four points GOLD

Area of square = (where D is the Diagonal)

Area =

Area = 24.5 cm²