Area - triangles, quadrilaterals, compound shapes

problem
Favourite

Kite in a Square

Age

14 to 18

Challenge level

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

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

So Big

Age

16 to 18

Challenge level

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

Dotty Triangles

Age

11 to 14

Challenge level

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
problem

Golden Triangle

Age

16 to 18

Challenge level

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.
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Diagonals for Area

Age

16 to 18

Challenge level

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

Kissing Triangles

Age

11 to 14

Challenge level

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

Biggest Enclosure

Age

14 to 16

Challenge level

Three fences of different lengths form three sides of an enclosure. What arrangement maximises the area?
problem

Maths Filler 2

Age

14 to 16

Challenge level

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

At a Glance

Age

14 to 16

Challenge level

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