Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### Advanced mathematics

### For younger learners

# Equilateral Areas

## You may also like

### Some(?) of the Parts

### Ladder and Cube

### At a Glance

Or search by topic

Age 14 to 16

Challenge Level

*ABC* and *DEF* are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of *ABC* and *DEF* .

Does this work for any whole number side lengths?

If not, under what circumstances does it work?

What if the lengths of the sides of the triangles had been *a* and *b* instead of 3 and 4?

Can you construct an equilateral triangle whose area is the sum of the areas of *ABC* and *DEF*? What is the new area?

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?