Draw a quad ABCD in which AB=3 8cm, BC=6 2cm, AD=8cm, b=90o and CD//AB Also construct a triangle equal in - Maths - Constructions

Question

Draw a quad ABCD in which AB=3 8cm, BC=6 2cm,
AD=8cm,<b=90o and CD//AB Also construct a triangle
equal in area to quad ABCD

Ishwarmani · Accepted Answer

Dear
Student,
Please find
below the solution to the asked query:

Given: In quadrilateral ABCD with AB||CD, AB=3
8 cm,BC=6
2 cm,AD=8 cm and ∠B=90°Since, AB||CDSo, ∠B+∠D=180°         Pair of consecutive interior angles⇒90°+∠D=180°⇒∠D=180°-90°=90°To construct: The quadrilateral ABCD and a triangle equal in area to quadrilaeral ABCDSteps of construction:1
 Draw AB=3 8 cm 2
 At point B, make ∠ABX=90° 3
 With B as centre, draw an arc of radius 6 cm to cut the ray BX at point C
4  At point C, make ∠YCB=90° 5
 With A as centre, draw an arc of radius 8 cm to cut the ray CY at point D
6  Join AD
Thus, ABCD is the required quadrilateral 7
 With A as centre, draw an arc of radius 4 cm to cut AD at point O
8
 Now join CO and extend it to intersect BA produced to point E
Thus, ∆CBE is the required triangle equal equal in arae to quadrilateral ABCD
Verification:In ∆AOE and ∆DOC,∠OAE=∠CDO     Alternate interior anglesAO=DO                  By construction, step 7∠AOE=∠DOC     Vertically opposite anglesSo, by ASA congruence critera,∆AOE≅∆DOC⇒ar∆AOE=ar∆DOC⇒ar∆AOE+arABCO=ar∆DOC+arABCO∴ ar∆CBE=arABCDNote: Many different triangles can be drawn with equal in area to quadrilateral ABCD

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Draw a quad ABCD in which AB=3.8cm, BC=6.2cm, AD=8cm,<b=90o and CD//AB.Also construct a triangle equal in area to quad ABCD.

Draw a quad ABCD in which AB=3.8cm, BC=6.2cm, AD=8cm,<b=90^oand CD//AB.Also construct a triangle equal in area to quad ABCD.