Spot the Hidden Triangle! | Olympiad Math

A rectangle has area 10 cm². Two midpoints and two crossing segments create a shaded region. Can you find its area without calculating any side lengths? Draw one diagonal, recognise the medians of a hidden triangle, and use the centroid to solve the problem quickly. Then see why the equal-area property works, using equal bases, shared heights and subtraction. Pause and try the question first. The visual solution keeps the diagram and matching expressions together, followed by a graphical summary of the steps. What you will learn: How to spot a useful diagonal in a shaded-area problem. What a median and a centroid mean. Why joining a centroid to the vertices gives three equal-area triangles. How to prove equal areas using common perpendicular heights. Why this shaded region is always two thirds of the rectangle. If you found this video useful, like this video and subscribe for more visual maths lessons. Chapters 0:00 Find the shaded area 0:20 PAUSE 0:37 Draw one useful diagonal 0:58 Spot the two medians 1:21 The fast calculation 1:43 Why equal areas? Use E 2:13 Why equal areas? Use F 2:37 Three equal pieces 3:02 Summary of steps 3:23 More visual maths lessons #OlympiadMath #Geometry #ShadedArea