ABCD is a parallelogram, Area(DAB)=a)3/4 [Ar (||gmABCD)]b)1/4 [Ar (||gmABCD)]c)2A(||gmABCD)d)1/2 [Ar (||gmABCD)]Correct answer is option 'D'. Can you explain this answer?

Question

Answer

ABCD is a parallelogram
In a Triangle ABC and ADC
AB=CD(opposite lines of a parallelogram)
BC=AD(opposite lines of a parallelogram)
AC=AC(common)
Triangle ABC and ADC ( SSS Cong. rule)
ar(ABC) =ar(ADC)=1/2 ar (ABCD)
hence proved

Answer

As the diagonal of a parallelogram divides it into two triangles of equal area. So, option D is correct.

Answer

Solution:

Given: ABCD is a parallelogram.

To find: Area(DAB) = ?

Explanation:

A parallelogram is a quadrilateral in which opposite sides are parallel and congruent.

Since ABCD is a parallelogram, the opposite sides AB and CD are parallel and congruent, and the opposite sides AD and BC are parallel and congruent.

Area of a parallelogram = base * height

Let's consider the base of the parallelogram as AB.

Now, draw a perpendicular from point D to line AB and let it intersect AB at point E.

This perpendicular line DE is the height of the parallelogram.

Since DE is perpendicular to AB, it forms a right angle at point E.

Now, we can see that triangle DAB is a right triangle with base AB and height DE.

Area of triangle DAB = (1/2) * base * height = (1/2) * AB * DE

But since DE is the height of the parallelogram, it is equal to the distance between the parallel lines AB and CD.

So, DE = CD

Therefore, the area of triangle DAB = (1/2) * AB * CD

Since AB and CD are parallel lines, they have the same length. So, AB = CD.

So, the area of triangle DAB = (1/2) * AB * AB = (1/2) * AB^2

But AB is the base of the parallelogram, and the area of a parallelogram is given by base * height.

So, the area of the parallelogram ABCD = AB * DE = AB * CD

Now, comparing the area of triangle DAB and the area of parallelogram ABCD, we can write:

Area(DAB) = (1/2) * AB^2 = (1/2) * [Area(ABCD)]

Therefore, the area of triangle DAB is half the area of parallelogram ABCD.

Hence, the correct answer is option 'd' - 1/2 [Ar (||gmABCD)].

Answer

ABCD is a parallelogram
In a Triangle ABC and ADC
AB=CD(opposite lines of a parallelogram)
BC=AD(opposite lines of a parallelogram)
AC=AC(common)
Triangle ABC and ADC ( SSS Cong. rule)
ar(ABC) =ar(ADC)=1/2 ar (ABCD)
Hence proved.

Similar Class 9 Doubts

P and Q are the points on AB and BCrespectively of gm ABCD, then

ABCD and FECG are parallelograms equal in area. If ar(AQE) = 12cm2, then ar(parallelogram FGBQ) =

If E, F,G and H are respectively the mid-points of the sides of a parallelogram ABCD, then ar(EFGH)is equal to

Point O is the point of intersection of AC and BD of parallelogram ABCD and, also,PQ AD, then,

In fig abcd and abef are parallelogram. The area of the parallelogram abcd is 90sq cm . find. (

Top Courses for Class 9View all

Science Class 9

Social Studies (SST) Class 9

Mathematics (Maths) Class 9

English Class 9

English Grammar Advanced

Top Courses for Class 9

Top Courses for Class 9

Suggested Free Tests

Related Content

Class 9 Study Material

Class 9 Subjects

Competitive Examinations for Class 9

NCERT Books

NCERT Solutions

Reference Books for Class 9

Other Popular Exams

Company