Question

Draw a rhombus of sides 6cms and one angle 60° and then draw a right angled triangle of the same area.​

Answer 1

Step-by-step explanation:

Step -1) At A, draw a line AQ so that angle (BAQ) = 60°. Step - 2) Cut AD at C such that AC = 6cm. Step - 3) At B, draw a BP so that angle (ABP) = 180° - 60° i.e. 120°. Step - 4) Cut BP at D such that BD = 6cm.

Answer 2

Answer:

Given :- Area of triangle = Area of Rhombus

Side of Rhombus 6 cm &one angle = 60°

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To Find :- Draw rhombus and triangle

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Solution :-

To Draw rhombus:-

Step 1 :- Draw a line segment AB' = 6cm

Step 2 :- Draw an angle of 60° at A on AB'

Step 3 :- Take same length of 6 cm from A on angle drawn & mark it C.

Step 4 :- Using compass , width = 6cm & taking C & B' as centre drawn two arcs interesting at D .

Step 5 :- Join CD & BD

Hence , Rhombus is constructed.

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Now ,

$\tt \: Area \: of \: Rhombus = {a}^{2} \sin\alpha$

$\tt \: = {6}^{2} \sin(60°)$

$\tt \: = 6 \times 6 \sin(60°)$

$\tt \: = \frac{1}{2} \times 12 \times 6 \sin(60°)$

∴ Area of Triangle

$\tt \: = \frac{1}{2} ab \sin\alpha$

$\tt \: = ( \frac{1}{2} ) \times 12 \times 6 \sin(60°)$

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Now , To Draw a triangle

Step 1 :- Draw a line segment AB = 12 cm

Step 2 :- Draw an angle of 60° using protractor at A on AB

Step 3 :- Take s length of 6 cm from A on angle drawn & mark as C.

Step 4 :- Join BC

Hence , ∆ABC is drawn .

∴ ∆ABC has same area as Rhombus whose side is 6 cm & one angle is 60°

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