Advertisements
Advertisements
प्रश्न
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.
उत्तर
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
संबंधित प्रश्न
ABCD is a trapezium in which AB || CD and AD = BC (see the given figure). Show that
- ∠A = ∠B
- ∠C = ∠D
- ΔABC ≅ ΔBAD
- diagonal AC = diagonal BD
[Hint: Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]
In the following figures, ABCD is a parallelogram.
find the values of x and y.
State, 'true' or 'false'
If two adjacent sides of a parallelogram are equal, it is a rhombus.
In the figure, given below, AM bisects angle A and DM bisects angle D of parallelogram ABCD. Prove that: ∠AMD = 90°.
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.
AD is a median of a ΔABC.P is any point on AD. Show that the area of ΔABP is equal to the area of ΔACP.
A quadrilateral ABCD is such that diagonals BD divides its area into two equal parts. Prove that BD bisects AC.
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
Find the area of each of the following figure:
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
One side of a parallelogram is 12cm and the altitude corresponding to i is 8cm. If the length of the altitude corresponding to its adjacent side is 16cm, find the length of the adjacent side.
A rectangular floor 45 in long and 12 m broad is to be paved exactly with square tiles, of side 60 cm. Find the total number of tiles required to pave it.
If a carpet is laid on the floor such as a space of 50 cm exists between its edges and the edges of the floor, find what fraction of the floor is uncovered.
A rectangular hall of 40m by 24m is covered with carpets of size 6m x 4m. Find the number of carpets required to cover the hall.
The perimeter of a square is 128cm and that of another is 96cm. Find the perimeter and the diagonal of a square whose area is equal to the sum of the areas of these two squares.
How many tiles, each of area 625 cm2, will be needed to pave a footpath which is 1 m wide and surrounds a grass plot of size 38 m x 14 m?
In quadrilateral ABCD, ∠A + ∠D = 180º. What special name can be given to this quadrilateral?
All the sides of a rhombus are of equal length.
Examine whether the following is a polygon. If it is not, say why?
Name polygon.
Make two more examples of this.
