Question

Prove that the area of a rhombus is equal to half of the product of its diagonals

Answer 1

let two diagonals be a,b.

diagonals in rhombus bisect perpendicularly.

Draw a rhombus and join opposite vertexes(diagonals)

here four triangles are formed.

all triangles are right angled(diagonals bisect perpendicularly)

select any one triangle.

two sides are known .

one is a/2,another is b/2.

area of triangle is 1/2×base ×height

=1/2×a/2×b/2=ab/8

there are four triangles like this with same area.

area of rhombus =4×area of one triangle

=4×ab/8=ab/2

area of rhombus =half of product of diagonals