Missing triangle in a square
A point inside a square or a rectangle is joined to all four corners, cutting it into four triangles, one on each side. Most questions give three of the triangles' areas and ask for the fourth. Others ask for the area of the whole shape, or give the side lengths and one triangle and ask for the triangle opposite it.
There isn't enough to work out where the point is, and there doesn't need to be. The triangles on opposite sides always make half the shape: lines across and down through the point cut it into four small rectangles, and each line to a corner cuts one of those in half. So top + bottom = left + right, and the step-by-step working colours the halves to show why.
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What changes each time
- Three forms: the missing triangle, the whole area, or one triangle from the side lengths
- Squares and rectangles, as a plain diagram (in cm² or bare numbers) or a garden of flower beds in m²
- Mostly two-digit areas in the diagrams, up to a few hundred m² in the gardens, with the point anywhere from a fifth to four fifths of the way across
More area, perimeter and volume practice
- Area by counting squares (Grade 2)
- Area and perimeter of a square (Grade 3)
- Area and perimeter of a rectangle (Grade 3)
- Area with half squares (Grade 3)
- Area of an L-shape (Grade 3)
- Perimeter of an L-shape (Grade 3)
- Draw a rectangle with a given area and perimeter (Grade 3)
- Missing side of a rectangle (Grade 4)
- Rectangle sides from a ratio (Grade 4)
- Area of a right triangle (Grade 4)
- Area of an isosceles triangle (Grade 4)
- Area of a scalene triangle (Grade 4)
- Area of an irregular polygon (Grade 5)
- Volume by counting cubes (Grade 5)