Step by step
The question
Question: find the area of a rhombus with diagonals 2.4 and 5.
1 Draw the box
A rhombus has four equal sides.
The marks show them.
The dashed lines join opposite corners.
They are the diagonals.
The diagonals cross at a right angle.
Draw a box around the rhombus.
It is 2.4 across and 5 up and down: the same as the diagonals.
The box is a rectangle.
Its area is 2.4 × 5.
2.4 times 5 is 12.
2 Take half
The diagonals cut the rhombus into 4 triangles.
The 4 corners of the box outside are the same 4 triangles again.
So the rhombus is exactly half of the box: A = ½ × d₁ × d₂.
Careful!
12 is the whole box.
The rhombus is only half of it.
Half of the box: A = ½ × 12.
Half of 12 is 6 square units.
3 Check
Let's check another way.
Cut along the dashed line from top to bottom: two triangles.
Each has base 5 and height half of 2.4: 1.2.
Two of them: 2 times half is 1.
We get 6 square units again.
So the area is right!
Let's look back.
First: draw the box.
Then: take half.
Last: check.