Advertisements
Advertisements
Question
Trapezium given below; find its area.
Advertisements
Solution
In the given figure, we can observe that the non-parallel sides are equal and hence it is an isosceles trapezium.
Therefore, let us draw DE and CF perpendiculars to AB.
Thus, the area of the parallelogram is given by
AB = AE + EF + FB and CD = EF = 18 cm, we have
30 = AE + 18 + FB
⇒ 30 = AE + 18 + AE
⇒ 2AE + 18 = 30
⇒ 2AE = 30 - 18
⇒ 2AE = 12
⇒ AE = 6 cm
Now, consider the right angled triangle ADE.
AD2 = AE2 + DE2
⇒ 122 = 62 + DE2
⇒ 144 = 36 + DE2
⇒ DE2 = 144 - 36
⇒ DE2 = 108
⇒ DE = `sqrt( 36 xx 3 )`
⇒ DE = `6sqrt3`
Area( `square"ABCD" ) = "Area"( Δ"ADE" ) + "Area"( square "DEFC") + "Area"( Δ"CFB" )`
⇒ Area( `square"ABCD" ) = 1/2 xx 6 xx 6sqrt3 + 18 xx 6sqrt3 + 1/2 xx 6 xx 6sqrt3`
⇒ Area( `square"ABCD" ) = 6 xx 6sqrt3 + 18 xx 6sqrt3`
⇒ Area( `square"ABCD") = 144sqrt3`= 249.41 cm2
APPEARS IN
RELATED QUESTIONS
The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.
The length of a rectangle is twice the side of a square and its width is 6 cm greater than the side of the square. If the area of the rectangle is three times the area of the square; find the dimensions of each.
Trapezium given below; find its area.
A rectangular plot 85 m long and 60 m broad is to be covered with grass leaving 5 m all around. Find the area to be laid with grass.
A wire when bent in the form of a square encloses an area of 484 m2. Find the largest area enclosed by the same wire when bent to from:
- An equilateral triangle.
- A rectangle of length 16 m.
The length and the breadth of a rectangle are 6 cm and 4 cm respectively. Find the height of a triangle whose base is 6 cm and the area is 3 times that of the rectangle.
How many tiles, each of area 400 cm2, will be needed to pave a footpath which is 2 m wide and surrounds a grass plot 25 m long and 13 m wide?
A quadrilateral field of unequal has a longer diagonal with 140m. The perpendiculars from opposite vertives upon this diagonal are 20m and 14m. Find the area of the field.
In the following, find the value of ‘a’ for which the given points are collinear
(a, 2 – 2a), (– a + 1, 2a) and (– 4 – a, 6 – 2a)
If vertices of a quadrilateral are at A(– 5, 7), B(– 4, k), C(– 1, – 6) and D(4, 5) and its area is 72 sq. units. Find the value of k.
