Area - triangles, quadrilaterals, compound shapes

problem

Another triangle in a triangle

Age

16 to 18

Challenge level

Can you work out the fraction of the original triangle that is covered by the green triangle?
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