Interactive geometry

Area Concept Lab

Move it first. Explain what changed. Calculate last.

SEE

A leaning pencil does not get shorter.

Move the pencil. Watch its length and its vertical height.

height 7.2 cm pencil 10 cm
Pencil
10 cm
Height
7.7 cm
SEE

Slide the rows. Do we lose any tiles?

This begins as a rectangle made from unit tiles. Push the rows sideways.

5 rows 8 tiles across
tiles across8
rows high5
total tiles40
SEE

One diagonal makes two equal halves.

Start with something familiar: a rectangle. Then cut it along the diagonal.

base 6 height 4 12 12
whole rectangle 6 × 4 = 24 one triangle 24 ÷ 2 = 12
DO

Build an area of 48.

Change the base and height. Try to make exactly 48 square units.

8 × 6 = 48
SEE

Put the missing corner back.

A weird floor plan gets easier when you first imagine the rectangle it came from.

20 ft 25 ft 37 ft 25 ft 12 ft 45 ft
1

Whole rectangle: 45 × 37 = 1665

2

Missing corner: 25 × 25 ÷ 2 = 312.5

3

Floor: 1665 − 312.5 = 1352.5 ft²

DO

Do not stop one step early.

After every calculation, name what you just found.

A triangle's base is 6 cm less than its height. Its height is 18 cm. What is the area?

height
18
base
?
← 6 cm shorter →
1

Find the missing base.

18 − 6 =
2

What did you just find?

3

The question asks for area. Finish the problem.

cm²
CHECK

What did I just find? Is that the thing the question actually asked for?