Question

draw a square ABCD whose area is 100cm^2 taking CD as base construct a parallelogram CDEF such that the perimeter of ABCFEDA is 80cm and angle CDE=50degree

Answer 1

Construction of square : -

1. Draw line CD = 10 cm { area of square = (side)^2= 100, side = 10cm} and extend this line .

2. Set the compass on c and any convenient draw the arc above the point C and without changing the compasses set the point P and Q.crossing the previous arc and create a point(let V). Join this point to C.

Set the compasses on D and set its width CD . Draw an arc above point D . Without changing the compases move the compass to point C. and draw an arc across CV , creating point B.

Similarly creates point A .
And then join D to A , C to B and A to B . Now , ABCD is a square .

Construction of parallelogram .

1. Here already constructed CD =10 cm . Now draw 50 degree angle at point D { we can't draw 50 degree by compass . Use protractor.}

2. Construct a line sigment DE= 20 cm { because ABCEFDA = 80 cm , AB + BC + DA = 30 cm . Rest 50 cm = DE + EF + CF . Let DE and CF are 20 cm then its possible} on the other arm of angle . Then, place the sharp point of coompasses at C and make an arc 5 cm .

Strech your compases at 10cm . Place the sharp end at point E and draw an arc to intersect an arc drawn in step 2.lebel the intersecting point F. Now join all point .

Here, CDEF is a parallelogram.

Done construction//