Calculating length of 1 side of a rhombus and its area!

Question

ABCD is a rhombus in the diagonal BD=10cm and diagoanl AC=12cm and AB=x cm!
Calculate:
(1)x^2

(2)the area of ABCD

Answer 1

the diagonals of a rhombus are perpendicular to each other and they also bisect each other

call the point of intersection of the diagonals point E

you have a right triangle AEB with AB the hypotenuse

AE=5 cm and BE=6 cm

using the Pythagorean Theorem

AB^2=5^2+6^2

AB^2=25+36

AB^2=61

if AB=x then x^2=61

 

the area of a rhombus is given by the formula A=(1/2)(d1)(d2) where d1 and d2 are the diagonals

A=(1/2)(12)(10)

A=(1/2)(120)   (or 1/2 * 12=6 and 6*10=60)

A=60 square cm