Free 11+ maths practice question: Two triangles in a rectangle
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ABCD is a rectangle 12 cm long and 7 cm high. P is a point on the top side, 4 cm from D, and the triangle APB is shaded. What is the total area of the two white triangles?
💡 Hints
Triangles in the corners of a rectangle
Area of a right-angled triangle = ½ × base × height.
If a shaded triangle uses the whole bottom side and touches the top, it is half the rectangle, so the white parts are the other half.
A missing base is the whole side minus the part you know.
Rectangle 10 by 6, P 3 cm along the top: left ½×3×6 = 9, right ½×7×6 = 21 → ?
🗝️ Key method: Two right-angled triangles, second base derived
Left: ½ × 4 × 7 = 14 cm².
Right base 12 − 4 = 8; ½ × 8 × 7 = 28.
14 + 28 = 42 cm².
1
The left white triangle ADP has base DP = 4 cm and height AD = 7 cm, so its area is ½ × 4 × 7 = 14 cm².
2
The right white triangle PCB has base PC = 12 − 4 = 8 cm and the same height, so its area is ½ × 8 × 7 = 28 cm².
3
Together the white triangles cover 14 + 28 = 42 cm², half of the 84 cm² rectangle. That must happen: the shaded triangle has base 12 and height 7, so it is 42 cm² wherever P sits.
🎉 Answer: C. 42 cm²
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