Step by step
The question
Question: find the area of a kite with diagonals 12 and 8.
1 Draw the box
A kite has two pairs of equal sides, side by side.
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 kite.
It is 12 across and 8 up and down: the same as the diagonals.
The box is a rectangle.
Its area is 12 × 8.
12 times 8 is 96.
2 Take half
The diagonals cut the kite into 4 triangles.
The 4 corners of the box outside are the same 4 triangles again.
So the kite is exactly half of the box: A = ½ × d₁ × d₂.
Careful!
96 is the whole box.
The kite is only half of it.
Half of the box: A = ½ × 96.
Half of 96 is 48 square units.
3 Check
Let's check another way.
Cut along the dashed line from top to bottom: two triangles.
Each has base 8 and height half of 12: 6.
Two of them: 2 times half is 1.
We get 48 square units again.
So the area is right!
Let's look back.
First: draw the box.
Then: take half.
Last: check.