Question

find the area of a rhombus over side of which measures 20cm and one of whose diagonals is 24cm

Answer 1

Hey there!

The formula for the area of a rhombus = ( 1 ÷ 2 ) × ( diagonal 1 ) × ( diagonal 2 )

We can use the pythagorean theorem :

We know,

Pythagorean Theorem!

H² = B² + P²

(AB)² = (OA)² + (OB)²

(20)² = (OA)² + (12)² ( 12 because half of 24 as the diagonal bisect each other )

400 = (OA)² + 144

400 - 144 = (OA)²

256 = (OA)²

16 cm = OA

Then,

AC = 2 x 16

= 32 cm

The other diagonal is 32 cm

If we substitute these values,

we get,

( 1 ÷ 2 ) × ( 24 ) × ( 32 )

( 1 ÷ 2 ) × ( 768 )

384 cm² is the area

Hope my answer helps!

#BeBrainly

@sid071

Answer 2

Answer:

A = 384cm²

a = Side = 20cm

p = Diagonal = 24 cm

a = pq / 2

a = p² + q² / 2

a = 1 / 2 p √4² - p²

= 1 / 2 • 24 • √ 4.20² - 24² = 384 cm³