One figure, three shapes

The figure is made up of Rectangle A B E D and Triangle B C E. A B is fourteen centimetres, A D is nine centimetres and D C is twenty centimetres. Find the area of the figure. Try it first. Pause if you like. We can add the rectangle and the triangle. First, which length belongs to the triangle? Separate the two parts along B E. The outside length is not the base of the triangle. D E equals A B, fourteen centimetres. D C is D E plus E C, twenty centimetres. E C is twenty minus fourteen, which is six centimetres. Area of a rectangle is length times breadth. The rectangle is fourteen times nine, which is one hundred and twenty six square centimetres. For triangle B C E, E C is the base. B E is the height, nine centimetres. They meet at a right angle. Area of a triangle is one half times base times height. Half of six is three. Three times nine is twenty seven square centimetres. Put the two parts back together. Their areas are added because both are inside the figure. One hundred and twenty six plus twenty seven is one hundred and fifty three square centimetres. The whole figure is the sum of these two parts. Each triangle needs its own base and height.

Rahim has a rectangular card P Q R S with P Q is twenty six centimetres and Q R is fourteen centimetres. T is a point on P Q with P T is nine centimetres. He cuts off Triangle P T S along T S. Find the area of the piece he has left. Try it first. Pause if you like. Start with the whole card. Then subtract the corner that Rahim cuts off. Area of a rectangle is length times breadth. Twenty six times fourteen is three hundred and sixty four square centimetres. Lift the corner triangle away along T S. We need the area of that corner. P T is the base, nine centimetres. P S is the height, fourteen centimetres. They meet at a right angle. Area of a triangle is one half times base times height. Half of fourteen is seven. Nine times seven is sixty three square centimetres. Put the corner back for a moment. The part we want is the whole card minus this triangle. Three hundred and sixty four minus sixty three is three hundred and one square centimetres. Add the parts that make a figure. Subtract the part removed from a whole.