Question

solve these qusn 4 ,5,6,7,8

Answer 1

$\large \tt AHOY!! \:$

4. ATQ, the base of a parallelogram is twice it's height.

let the height be 'x'

therefore base = 2x

given the area of the parallelogram = 288cm²

therefore b × h = 288cm²

=> x × 2x = 288cm²

=> 2x² = 288cm²

=> x² = 288/2

=> x² = 144

=> x = √144

=> x = 12cm

hence, the height of the parallelogram is = x = 12cm

and base of the parallelogram is = 2x = 2 × 12 = 24cm

5. given :-

AD = 8cm

DC = 12cm

let the point where A is bisecting AC be O.

given AO = 6cm

the formula for finding the area of a parallelogram is b × a

where 'b' is any of the side of the parallelogram and 'a' is the corresponding altitude.

let's take the base as DC = 12cm

and therefore altitude = AO = 6cm

(i) area of the parallelogram = 12 × 6

= 72cm²

now if we take the base as AD and altitude as CL, then the area will be same.

(ii) AD × CL = 72cm²

=> 8 × CL = 72cm²

=> CL = 72/8

=> CL = 9cm

6. the formula for finding the area of a rhombus is = 1/2 × d1 × d2

where d1 and d2 are the diagonals of the Rhombus.

given :-

d1 = 24cm

d2 = 20cm

therefore area of the rhombus = 1/2 × d1 × d2

= 1/2 × 24 × 20

= 12 × 20

= 240cm²

7. given perimeter of the rhombus = 60cm

therefore 4 × side = 60cm (since all sides of a rhombus is equal)

=> side = 60/4

=> side = 15cm

now, it's given that the area of the Rhombus is 207cm. and we have to find it's height.

always remember that rhombus is a parallelogram and we can use 'b × h' formula also to find it's area. if we have to find the side or height of the rhombus and area is given, then use 'b × h' formula for solving. if we have to find the diagonals, then use '1/2 × d1 × d2'

here we have to find the height. so we will use 'b × h' and 'b' is the side of the Rhombus.

=> b × h = 207cm²

=> 15 × h = 207cm²

=> h = 207/15

=> h = 13.8cm

hence, the altitude (height) of the Rhombus is 13.8cm

8. given :-

area of the rhombus = 96cm²

d1 = 12cm

d2 = ?

here we have to first find the diagonal.

so we will use '1/2 × d1 × d2' formula

=> 1/2 × d1 × d2 = 96cm²

=> 1/2 × 12 × d2 = 96cm²

=> 6 × d2 = 96cm²

=> d2 = 96/6

=> d2 = 16cm

now we have to find it's side to find the perimeter.

by Pythagoras theorem,

=> side² (hypotenuse) = (d1/2)²(base) + (d2/2)²(perpendicular)

=> side² = 6² + 8²

=> side² = 36 + 64

=> side² = 100

=> side = √100

=> side = 10cm

hence, perimeter of the Rhombus = 4 × side

= 4 × 10

= 40cm

note : I used 'b × a' somewhere and also 'b × h'. both are same. h = a (height = altitude)
don't get confused :-)

$\large \tt HOPE \: THIS \: HELPS!!$