Advertisements
Advertisements
Question
In the given figure, if AB ∥ DC ∥ FG and AE is a straight line. Also, AD ∥ FC. Prove that: area of ∥ gm ABCD = area of ∥ gm BFGE.
Solution
Joining AC and FE, we get
ΔAFC and ΔAFE are on the same base AF and between the same parallels AF and CE.
⇒ A(ΔAFC) = A(ΔAFE)
⇒ A(ΔABF) + A(ΔABC) = A(ΔABF) + A(ΔBFE)
⇒ A(ΔABC) = A(ΔBFE)
⇒ `(1)/(2)` A(parallelogram ABCD)
= `(1)/(2)`A(parallelogram BFGE)
⇒ A(parallelogram ABCD)
= A(parallelogram BFGE).
APPEARS IN
RELATED QUESTIONS
If the diagonals of a parallelogram are equal, then show that it is a rectangle.
ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that:
- ABCD is a square
- diagonal BD bisects ∠B as well as ∠D.
ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (See the given figure). Show that
- ΔAPB ≅ ΔCQD
- AP = CQ
State, 'true' or 'false'
The diagonals of a quadrilateral bisect each other.
ABCD is a parallelogram having an area of 60cm2. P is a point on CD. Calculate the area of ΔAPB.
In the given figure area of ∥ gm PQRS is 30 cm2. Find the height of ∥ gm PQFE if PQ = 6 cm.
In the given figure, BC ∥ DE.
(a) If area of ΔADC is 20 sq. units, find the area of ΔAEB.
(b) If the area of ΔBFD is 8 square units, find the area of ΔCEF
If the medians of a ΔABBC intersect at G, show that ar(ΔAGB) = ar(ΔAGC) = ar(ΔBGC) = `(1)/(3)"ar(ΔABC)"`.
In the given figure, ABC is a triangle and AD is the median.
If E is any point on the median AD. Show that: Area of ΔABE = Area of ΔACE.
In the given figure, ABC is a triangle and AD is the median.
If E is the midpoint of the median AD, prove that: Area of ΔABC = 4 × Area of ΔABE
Two adjacent sides of a parallelogram are 34 cm and 20 cm. If one of its diagonal is 42 cm, find: distance between its shorter sides
Find the perimeter and area of a square whose diagonal is `5sqrt(2)"cm"`. Give your answer correct to two decimal places if `sqrt(2)` = 1.414.
The perimeter of a square plot of land is 64m. The area of a nearby rectangular plot is 24m2 more than the area of the given square. If the length of the rectangle is 14m, find its breadth.
The side of a square exceeds the side of another square by 4cm and the sum of the areas of the squares is 400cm2. Find the dimensions of the squares.
Find the area of a rhombus whose perimeter is 260cm and the length of one of its diagonal is 66cm.
A rectangular field is 240m long and 180m broad. In one corner a farm house is built on a square plot of side 40m. Find the area of the remaining portion and the cost of fencing the open sides Rs.25per m.
ABCD is a trapezium in which AB || DC and ∠A = ∠B = 45º. Find angles C and D of the trapezium.
The opposite sides of a rectangle are equal in length.
Give reason for the following :
Square is also a parallelogram.
