Question

If a RHOMBUS od each side measuring 100cm and has one of its

diagonal measuring 160 cm than find its area.​

Answer 1

Answer:

All four sides of a rhombus are equal hence join the given diagonal of 160cm160cm to divide the rhombus into two congruent triangles each having sides 160,100,100160,100,100

Now, using Hero’s formula for area of triangle with sides a=160,b=100,c=100(s=(160+100+100)/2=180)a=160,b=100,c=100(s=(160+100+100)/2=180)

=s(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−−√=s(s−a)(s−b)(s−c)

=180(180−160)(180−100)(180−100)−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√=180(180−160)(180−100)(180−100)

=4800 cm2=4800 cm2

∴ area of rhombus=2×(area of triangle)∴ area of rhombus=2×(area of triangle)

=2(4800)=2(4800)

=9600 cm2

Answer 2

SOLUTION:

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ANSWER:

• Area of the Rhombus = 9600cm².

TO FIND:

• Area?

GIVEN:

• RHOMBUS of each side measuring 100cm.
• Diagonal measuring 160 cm.

SOLUTION:

Let the area be x

Let's use herons formula to find the area of the rhombus using the sides = 100,100,160

Now,

by applying this formula we will get the area of the triangle.

FORMULA TO FIND:

Herons formula = √s( s - a )( s - b )( s - c )

• A = 160
• B = 100
• C = 100
• S = 180

SOLVING BY APPLYING THE FORMULA:

= √180( 180 - 160 )( 180 - 100 )( 180 - 100 )

= √180( 20 )( 80 )( 80 )

= √180 × 20 × 80 × 80

= √180 × √20 × √80 × √80

= 4800cm.

Now,

Area of rhombus = 2 × Area of a triangle

Area of rhombus = 2 × 4800cm²

Area of rhombus = 9600cm²

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