Q. 1 B5.0( 5 Votes )

# Calculate the areas of the parallelograms shown below:

Consider a parallelogram ABDC.
Let us draw a perpendicular on base AB from C say, CE.

Let length of AE = x cm and CE = y cm.

In Δ AEC:

CAE = 60° and CEA = 90°
ACE = 30° ( C + E + A = 180° )

We know that sides of any triangle of angles 30°, 60° and 90°
are in the ratio 1:√3:2.

x:y:2 = 1:√3:2
x = 1 cm and y = √3 cm

OR
We can consider Δ AEC as a half of equilateral Δ ACL.

Since, Δ ACL is an equilateral triangle.
We get,

AL = AC
(x + x) = 2 cm
2x = 2 cm
x = 1 cm

Using the Pythagoras theorem in Δ AEC ,
we get,

AC2 = AE2 + EC2
(2)2 = (1)2 + (y)2
4 - 1 = (y)2
(3) = (y)2
y = √3 cm

CE = √3 cm and also line segment CE is a height of parallelogram ABDC.
Also base AB = 4 cm.

Thus area of parallelogram = base × height

area (ABDC) = 4 × √3 cm2 = 4√3 cm2

Area = 4√3 cm2

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz | Trigger on Trigonometry47 mins
Basics of TrigonometryFREE Class
NCERT | Trigonometric Identities52 mins
Champ Quiz | Trigonometry Important Questions33 mins
Solving NCERT Questions on Trigonometric Identities56 mins
Trick to learn all Trigonometric Formulae28 mins
Champ Quiz | NTSE Trigonometry50 mins
Testing the T- Ratios of Specified Angles57 mins
Foundation | Cracking Previous Year IMO QuestionsFREE Class
NCERT | Imp. Qs. on Trigonometry42 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses