Question

Construct the following quadrilaterals
A) Quadrilateral LIFT
\[{\text{LI}} = 4{\text{ cm}}\]
\[{\text{IF}} = 3{\text{ cm}}\]
\[{\text{TL}} = 2.5{\text{ cm}}\]
\[{\text{LF}} = 4.5{\text{ cm}}\]
\[{\text{IT}} = 4{\text{ cm}}\]
B) Quadrilateral GOLD
\[{\text{OL}} = 7.5{\text{ cm}}\]
\[{\text{GL}} = 6{\text{ cm}}\]
\[{\text{GD}} = 6{\text{ cm}}\]
\[{\text{LD}} = 5{\text{ cm}}\]
\[{\text{OD}} = 10{\text{ cm}}\]

Answer 1

Hint: First we will draw side EA of length 5 cm and then we will mark point I, take 4 cm as radius and L as the centre, draw an arc on top of LF and then we will take 3 cm as the radius, F as the centre, draw an arc on top of LF and then mark point T, take 4 cm as radius and I as the centre, draw an arc on bottom of LF and then we will take \[2.5\] cm as the radius, L as the centre, draw an arc on bottom of LF and then join LI, IF, FT, LT, IT for part (i). Follow similar steps for the part (ii) and (iii).

Complete step by step solution:
First, we will draw side LF of length \[4.5\] cm, we get

Now, we will mark point I, take 4 cm as radius and L as the centre, draw an arc on top of LF and then we will take 3 cm as the radius, F as the centre, draw an arc on top of LF, we get

We will now mark point T, take 4 cm as radius and I as the centre, draw an arc on bottom of LF and then we will take \[2.5\] cm as the radius, L as the centre, draw an arc on bottom of LF, we get

Joining LI, IF, FT, LT, IT and then labelling the sides, we get

B) First, we will draw side GL of length 6 cm, we get

Now, we will mark point O, take \[7.5\] cm as radius and L as the centre, draw an arc on top of GL and then we will take 10 cm as the radius, D as the centre, draw an arc on top of GL, we get

We will now mark point D, take 6 cm as radius and G as the centre, draw an arc on bottom of GL and then we will take 5 cm as the radius, L as the centre, draw an arc on bottom of GL, we get

Joining GO, OL, LD, GD, OD and then labelling the sides, we get

Note: In solving these types of questions, students need to read the question properly before writing. Students have to be precise while drawing the lengths and angles properly as this is a crucial part of the problem. Remembering the steps for the construction problem is important.