Step by step
The question
Question: find the area of a rhombus with diagonals 7 m and 5 m.
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 7 m across and 5 m up and down: the same as the diagonals.
The box is a rectangle.
Its area is 7 × 5.
7 times 5 is 35.
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!
35 is the whole box.
The rhombus is only half of it.
Half of the box: A = ½ × 35.
Half of 35 is 17.5 m².
3 Check
Let's check another way.
Cut along the dashed line from top to bottom: two triangles.
Each has base 5 m and height half of 7: 3.5.
Two of them: 2 times half is 1.
We get 17.5 m² again.
So the area is right!
Let's look back.
First: draw the box.
Then: take half.
Last: check.