Question

If each side of the rhombus is 40 m and its longer diagonal is 48 m, then the area of rhombus is

Answer 1

Answer:

The side length of a rhombus is 40 and one of the diagonals is 48. What is the area of the rhombus?

Solution: Method 1: Side of the rhombus = 40. This is the hypotenuse of the RAT.

One side of the RAT = 48/2 = 24

Other side of the RAT = (40^2–24^2)^0.5 = 32.

So the are of the rhombus = 4 times the area of each RAT = 4 *(24*32)/2 = 1536 sq. units.

Method 2: If one diagonal is 48, the other diagonal is 64. SO the area pf the rhombus = d1*d2/2 = 48*64/2 = 1536 sq. units.

Method 3: Area of one triangle with sides 40, 40 and 48:

2s + 40+40+48 = 128, or s = 64

Heron’s formula give the area as [64*24*24*16]^0.5 = 768.

Area of the rhombus = 2*768 = 1536 sq. units.

Answer 2

Answer:

if each side of the rhombus is 40 m and its longer diagonal is 48 m then the area of rhombus is