RD Chapter 15 Areas of Parallelograms and Triangles Ex 15.2 Solutions
Question - 1 : - If the given figure, ABCD is aparallelogram, AE ⊥ DC and CF ⊥ AD. If AB =16 cm. AE =8 cm and CF =10 cm, find AD.
Answer - 1 : -
Given: Here in the question it is given
(1) ABCD is a parallelogram,
(2)
and(3)
, AB = 16 cm(4) AE = 8cm
(5) CF = 10cm
To Find : AD =?
Calculation: We know that formula for calculating the
Therefore,
Area of paralleogram ABCD = DC × AE (Taking base as DC and Height as AE )
Area of paralleogram ABCD = AB × AE (AB = DC as opposite side of the parallelogram are equal)
Therefore,
Area of paralleogram ABCD = 16 × 8 ……(1)
Taking the base of Parallelogram ABCD as AD we get
Area of paralleogram ABCD = AD × CF (taking base as AD and height as CF)
Area of paralleogram ABCD = AD × 10 ……(2)
Since equation 1 and 2 both represent the Area of the same Parallelogram ABCD , both should be equal.
Hence fro equation (1) and (2),
This means that,
Hence we get the result as
Answer - 2 : -
Given: Here in the question it is given that
(1) ABCD is a parallelogram,
(2)
and(3)
(4) AD = 6 cm
(5) AE = 8cm
(6) CF = 10cm
To Find : AB =?
Calculation: We know that formula for calculating the
To Find : AB =?
Calculation: We know that formula for calculating the
Area of paralleogram = base × height
Therefore,
Area of paralleogram ABCD = DC × AE (Taking base as DC and Height as AE )
Area of paralleogram ABCD = AB × AE (AB = DC as opposite side of the parallelogram are equal)
Therefore, Area of paralleogram ABCd = 16 × 8
Area of Parallelogram ABCD = AB× 8 ……(1)
Taking the base of Parallelogram ABCD as AD we get
Area of paralleogram ABCD = AD × CF (taking base as AD and height as CF)
Area of paralleogram ABCD = 6 × 10 ……(2)
Since equation 1and 2 both represent the Area of the same Parallelogram ABCD , both should be equal.
Hence equation 1 is equal to equation 2
Which means that,
Hence we got the measure of AB equal to
Question - 3 : - Let ABCD be a parallelogram of area 124 cm2. If E and F are the mid-points of sides AB and CD respectively, then find the area of parallelogram AEFD.
Answer - 3 : -
Given: Here in the question it is given that
(1) Area of paralleogram ABCD = 124 cm2
(2) E is the midpoint of AB, which means
(3) F is the midpoint of CD, which means
To Find : Area of Parallelogram AEFD
Calculation: We know that formula for calculating the
Area of Parallelogram = base × height
Therefore,
Area of paralleogram ABCD = AB × AD (Taking base as AB and Height as AD ) ……(1)
Therefore,
Area of paralleogram AEFD = AE × AD (Taking base as AB and Height as AD ) ……(2)
(
)=
Area of Parallelogram ABCD (from equation1)Hence we got the result Area of Parallelogram AEFD
Question - 4 : - If ABCD is a parallelogram, then prove that
ar (ΔABD) = ar (ΔBCD) = ar (ΔABC) = ar (ΔACD) = 1212 ar (||gm ABCD)
Answer - 4 : -
Given: Here in the question it is given that
(1) ABCD is a Parallelogram
To Prove :
(1)
(2)
(3)
(4)
Construction: Draw
Calculation: We know that formula for calculating the
Area of Parallelogram = base × height
Area of paralleogram ABCD = BC × AE (Taking base as BC and Height as AE ……(1)
We know that formula for calculating the
Area of ΔADC =
Base × Height 
(AD is the base of ΔADC and AE is the height of ΔADC) =
Area of Parallelogram ABCD (from equation1)Hence we get the result
Similarly we can show that