Advertisements
Advertisements
Question
ABC is a triangle in which D is the mid-point of BC. E and F are mid-points of DC and AErespectively. IF area of ΔABC is 16 cm2, find the area of ΔDEF.
Solution
Given: Here from the given question we get
(1) ABC is a triangle
(2) D is the midpoint of BC
(3) E is the midpoint of CD
(4) F is the midpoint of A
Area of ΔABC = 16 cm2
To find : Area of ΔDEF
Calculation: We know that ,
The median divides a triangle in two triangles of equal area.
For ΔABC, AD is the median
Area of Δ ADC = `1/2 `(Area of ΔABC )
`=1/2 (16)`
= 8 cm2
Area of Δ ADC = 8cm2
For ΔADC , AE is the median .
Area of ΔAED = `1/2 ` (Area of Δ ABC)
`= 1/2 (8)`
= 4 cm2
Area of ΔAED = 4 cm2
Similarly, For ΔAED , DF is the median .
Area of ΔDEF = `1/2 ` (Area of Δ AED)
`= 1/2 (4)`
= 2 cm2
Area of ΔDEF = 2 cm2
Hence we get Area of ΔDEF = 2 cm2
APPEARS IN
RELATED QUESTIONS
In the below fig. ∠AOB = 90°, AC = BC, OA = 12 cm and OC = 6.5 cm. Find the area of
ΔAOB.
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 the given figure, ABCD is a rectangle in which CD = 6 cm, AD = 8 cm. Find the area of parallelogram CDEF.
The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm is ______.
The perimeter of a triangle ABC is 37 cm and the ratio between the lengths of its altitudes be 6: 5: 4. Find the lengths of its sides.
Let the sides be x cm, y cm, and (37 - x - y) cm. Also, let the lengths of altitudes be 6a cm, 5a cm, and 4a cm.
The length and breadth of a rectangular piece of land are in the ratio 5 : 3. If the total cost of fencing it at the rate of ₹24 per meter is ₹9600, find its :
(i) length and breadth
(ii) area
(iii) cost of levelling at the rate of ₹60 per m2.
By counting squares, estimate the area of the figure.
The table given below contains some measures of the rectangle. Find the unknown values.
| Length | Breadth | Perimeter | Area |
| 13 cm | ? | 54 cm | ? |
Which has the bigger area - one of your footprints or the page of this book?
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 other rectangles can he make with 100 meters of wire? Discuss which of these rectangles will have the biggest area.
