Quadrilaterals Class 8 Long Question Answer

Quadrilaterals Class 8 Long Question Answer

Quadrilaterals Class 8 Long Question Answer

Question 1.

Construct a trapezium ABCD in which AB [| DC, ∠A = 105°, AD = 3 cm, AB = 4 cm and CD = 8 cm.

Solution:

∠A + ∠D = 180°

105° + ∠D = 180°

∠D = 75°.

Steps of construction:

1. Draw AB = 4 cm.

2. Draw [latex]\overrightarrow{\mathrm{AX}}[/latex] such that ∠BAX = 105°.

3. Mark a point D on AX such that AD = 3 cm.

4. Draw [latex]\overrightarrow{\mathrm{DY}}[/latex] such that ∠ADY = 75°.

5. Mark a point C on DY such that CD = 8 cm.

6. Join BC.

ABCD is the required trapezium.

Question 2.

Construct a rhombus whose diagonals are 5.2 cm and 6.4 cm long.

Solution:

Let diagonal AC = 5.2 cm and diagonal BD - 6.4 cm.

Draw AC = 5.2 cm. Draw XY, the perpendicular

bisector of AC which cuts AC at O.

With O as centre, draw arcs of radii

[latex]\left(=\frac{\mathrm{BD}}{2}=\frac{6.4}{2} \mathrm{~cm}\right)[/latex] = 3.2 cm

which cut OX at D and OY at B.

Join AB, BC, CD and DA.

Then, ABCD is the required rhombus.