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
In fig below, ABCD is a parallelogram, AE ⊥ DC and CF ⊥ AD. If AB = 16 cm, AE = 8
cm and CF = 10 cm, find AD.
In a ΔABC if D and E are mid-points of BC and AD respectively such that ar (ΔAEC) = 4cm2, then ar (ΔBEC) =
ABCD is a trapezium in which AB || DC. If ar (ΔABD) = 24 cm2 and AB = 8 cm, then height of ΔABC is
Find the area of a square, whose side is: 4.5 cm.
Each side of a square is 7 m. If its each side be increased by 3 m, what will be the increase in its area.
Each line gives a story. You have to choose the question which makes the best story problem. The first one is already marked.
- 352 children from a school went on a camping trip. Each tent had a group of 4 children.
a) How many children did each tent have? b) How many tents do they need? c) How many children in all are in the school?
In the following figure, the area of parallelogram ABCD is ______.
The amount of region enclosed by a plane closed figure is called its ______.
Find the area of the following figure by counting squares:
What is the area of a closed shape?
