Question

6. Find the area ofa rhombus whose side is 5 cm and whose altitude i 4.8 cm. If one of its diagonals is 8 cm long,find the length of the other diagonal.(explain plse)

Answer 1

hiii!!!

here's ur answer...

given the side of the rhombus is 5cm and altitude is 4.8cm.

area of the rhombus is base × height.

base is the side of the rhombus and height is the altitude.

area = b × h

= 5 × 4.8

= 24cm²

now,

there is one more formula for finding the area of rhombus. that is 1/2 × d1 × d2 . d1 and d2 are diagonals.

given one of the diagonal of the rhombus is 8cm.

area of the rhombus = 24cm²

therefore 1/2 × d1 × d2 = 24cm²

==> 1/2 × 8 × d2 = 24cm²

==> 4 × d2 = 24cm²

==> d2 = 24/4

==> d2 = 6cm

VERIFICATION:-

area of the rhombus = 1/2 × d1 × d2

= 1/2 × 8 × 6

= 4 × 6

= 24cm²

hence verified

thus the another diagonal of the rhombus is 6cm.

hope this helps u...!!

Answer 2

area of rhombus=1/2*diagonal1*diagonal2

RHOMBUS is a special parallelogram

we can find area of rhombus by using the formula of area of parallelogram that is breadth*height because rhombus is a special parallelogram

area of rhombus=breadth*height
=5*4.8 sq cm
=24 sq cm
as we now know the area of rhombus we can find the length of the other diagonal as per the question.

area of rhombus=1/2*diagonal 1*diagonal2
24 sq cm =1/2*8cm*diagonal 2
24 sq cm =4cm*diagonal 2
24 sq cm/4cm =diagonal 2
6cm =diagonal 2

length of the other diagonal=6 cm

verification

area of rhombus=1/2*diagonal 1*diagonal2
=1/2*8cm*diagonal 2
=1/2*8cm*6cm
=1/2*48 sq cm
=24 sq cm