Area - triangles, quadrilaterals, compound shapes

problem
Favourite

Kite in a Square

Age

14 to 18

Challenge level

2 out of 3

Can you make sense of the three methods to work out what fraction of the total area is shaded?
problem
Favourite

Areas and Ratios

Age

16 to 18

Challenge level

2 out of 3

Do you have enough information to work out the area of the shaded quadrilateral?
problem
Favourite

So Big

Age

16 to 18

Challenge level

2 out of 3

One side of a triangle is divided into segments of length a and b by the inscribed circle, with radius r. Prove that the area is: abr(a+b)/ab-r^2
problem

Golden Triangle

Age

16 to 18

Challenge level

2 out of 3

Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio.
problem

Diagonals for Area

Age

16 to 18

Challenge level

2 out of 3

Can you prove this formula for finding the area of a quadrilateral from its diagonals?
problem

Kissing Triangles

Age

11 to 14

Challenge level

2 out of 3

Determine the total shaded area of the 'kissing triangles'.
problem

Maths Filler 2

Age

14 to 16

Challenge level

2 out of 3

Can you draw the height-time chart as this complicated vessel fills with water?
problem

At a Glance

Age

14 to 16

Challenge level

3 out of 3

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

Biggest Bendy

Age

16 to 18

Challenge level

3 out of 3

Four rods are hinged at their ends to form a quadrilateral. How can you maximise its area?
problem

Square Pizza

Age

14 to 16

Challenge level

3 out of 3

Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?