Step by step
The question
Question: find the area of a rhombus with diagonals 10 and 6.
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 10 across and 6 up and down: the same as the diagonals.
The box is a rectangle.
Its area is 10 × 6.
10 times 6 is 60.
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!
60 is the whole box.
The rhombus is only half of it.
Half of the box: A = ½ × 60.
Half of 60 is 30 square units.
3 Check
Let's check another way.
Cut along the dashed line from top to bottom: two triangles.
Each has base 6 and height half of 10: 5.
Two of them: 2 times half is 1.
We get 30 square units again.
So the area is right!
Let's look back.
First: draw the box.
Then: take half.
Last: check.