Advertisements
Advertisements
Question
If P is any point in the interior of a parallelogram ABCD, then prove that area of the
triangle APB is less than half the area of parallelogram.
Advertisements
Solution
Draw DN ⊥ AB and PM ⊥ AB.
Now,
`Area (ΙΙ^(gm) ABCD) = AB xx DN , ar (ΔAPB ) = 1/2 (AB xx PM)`
Now , PM < DN
⇒ `AB xx PM < AB xx DN`
⇒ ` 1/2 (AB xx PM) < 1/2 (AB xx DN)`
⇒ `Area ( ΔAPB ) <1/2 ar ( Parragram ABCD)`
APPEARS IN
RELATED QUESTIONS
Compute the area of trapezium PQRS is Fig. below.
ABCD is a parallelogram whose diagonals AC and BD intersect at O. A line through O
intersects AB at P and DC at Q. Prove that ar (Δ POA) = ar (Δ QOC).
D is the mid-point of side BC of ΔABC and E is the mid-point of BD. if O is the mid-point
of AE, prove that ar (ΔBOE) = `1/8` ar (Δ ABC).
In the below fig. X and Y are the mid-points of AC and AB respectively, QP || BC and
CYQ and BXP are straight lines. Prove that ar (Δ ABP) = ar (ΔACQ).
The medians of a triangle ABC intersect each other at point G. If one of its medians is AD,
prove that:
(i) Area ( ΔABD ) = 3 x Area ( ΔBGD )
(ii) Area ( ΔACD ) = 3 x Area ( ΔCGD )
(iii) Area ( ΔBGC ) = `1/3` x Area ( ΔABC ).
Find the area of a square, whose side is: 4.1 cm.
The table given below contains some measures of the rectangle. Find the unknown values.
| Length | Breadth | Perimeter | Area |
| 13 cm | ? | 54 cm | ? |
Look at a 10 rupee note. Is its area more than hundred square cm?
The region given in the following figure is measured by taking 
as a unit. What is the area of the region?
Which unit is used to express area?
