Shaded areas

Hello, and welcome to Myriora Maths! What is the area of the shaded part? It's an odd shape, so there's no single formula. But there's a simple trick!

Find the area of the whole rectangle: ten times eight is eighty square centimetres. Then find the area of the hole: four times three is twelve. The shaded area is the whole, take away the hole: eighty take away twelve is sixty-eight square centimetres.

Why do we take away? Area just counts squares: this rectangle has eighty. The hole takes twelve of those squares away. So sixty-eight squares are left.

Here's an L shape. You could split it into two rectangles: eight times four is thirty-two, and five times two is ten. Thirty-two plus ten is forty-two. Or take the whole rectangle, eight times six, which is forty-eight, and the missing corner, three times two, which is six. Forty-eight take away six is forty-two. Both ways give forty-two square centimetres!

This works for borders too. A photo, ten by seven, sits in a frame, twelve by nine. The frame's area is the whole, take away the photo: a hundred and eight take away seventy is thirty-eight square centimetres.

A common mistake is taking away the lengths instead of the areas. Ten take away four is six, eight take away three is five, and six times five is thirty. But the shaded part isn't a rectangle! Work out each area first, then take away: sixty-eight.

Your turn! A square, nine centimetres on each side, has a square hole, five centimetres on each side. What is the shaded area? You've got twenty seconds, or pause the video if you need more time. Go!

Time's up! The whole square is nine times nine: eighty-one. The hole is five times five: twenty-five. Eighty-one take away twenty-five is fifty-six square centimetres!

Quick review. The shaded area is the whole, take away the parts that aren't shaded. Or split the shape into rectangles, and add them. And always take away areas, never lengths. See you next time!