Advertisements
Advertisements
प्रश्न
ABCD is a parallelogram in which BC is produced to E such that CE = BC. AE intersects
CD at F.
(i) Prove that ar (ΔADF) = ar (ΔECF)
(ii) If the area of ΔDFB = 3 cm2, find the area of ||gm ABCD.
Advertisements
उत्तर
In triangles and , ADF ECF we have
∠ADF = ∠ECF [Alternative interior angles, Since || AD BE]
AD = EC [ Since AD = BC = CE ]
And ∠DFA = ∠CFA [vertically opposite angles]
So, by AAS congruence criterion, we have
ΔADF ≅ ECF
⇒ area (ΔADF) = area (ΔECF) and DF = CF.
Now, DF = CF
⇒ BF is a madian in ΔBCD
⇒ area (ΔBCD) =2ar (ΔBDF)
⇒ area (ΔBCD) = 2× 3 cm2 =6cm2
Hence, ar (||gm ABCD) = 2ar (ΔBCD) 2 × 6cm2
=12cm2
APPEARS IN
संबंधित प्रश्न
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.
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).
In a ΔABC if D and E are mid-points of BC and AD respectively such that ar (ΔAEC) = 4cm2, then ar (ΔBEC) =
What is the area of the rectangle? ________ square cm
The King was very happy with carpenters Cheggu and Anar. They had made a very big and beautiful bed for him. So as gifts the king wanted to give some land to Cheggu, and some gold to Anar. Cheggu was happy. He took 100 meters of wire and tried to make different rectangles.
He made a 10 m × 40 m rectangle. Its area was 400 square meters. So he next made a 30 m × 20 m rectangle.
- What is its area? Is it more than the first rectangle?
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?
Each line gives a story. You have to choose the question which makes the best story problem. The first one is already marked.
- A shopkeeper has 204 eggs. He puts them in egg trays. Each tray has 12 eggs.
a) How many more eggs will he need? b) How many fresh eggs does he sell? c) How many egg trays does he need?
The amount of region enclosed by a plane closed figure is called its ______.
How will you decide? Discuss.
Find the area of the following figure by counting squares:
