A composite figure is any shape built from two or more basic shapes — a rectangle topped by a semicircle, an L-shaped plot, a square with a triangular roof. The method never changes: cut the figure into pieces whose areas you can compute, find each, then add. The art is in the cut. Look for a horizontal or vertical line that splits the figure into clean rectangles and triangles; for curved parts, spot the circle, semicircle or sector hiding in the diagram. An L-shape can be handled two ways — split it into two rectangles, or take a big rectangle and subtract the missing corner. CAT often gives the figure verbally rather than drawn, so sketching it yourself is half the battle. Keep every length in the same unit before you start, and watch for shared edges — they do not get counted twice in area, only in perimeter.
✅ Solved examples
1. A figure is a rectangle 10 cm by 6 cm with a semicircle (diameter 6 cm) attached to one short side. Find its area. Use π ≈ 22/7.
3. A house wall is shaped as a 6 m wide rectangle of height 4 m topped by an isosceles triangle of base 6 m and height 2 m. Find the wall area.
Rectangle = 6 × 4 = 24. Triangle = ½ × 6 × 2 = 6. Total = 24 + 6 = 30 m².
4. A running lane cross-section is a rectangle 14 cm by 10 cm with a quarter-circle of radius 7 cm cut from one corner. Find the remaining area. Use π ≈ 22/7.
1. A rectangle 12 cm by 5 cm has a semicircle of diameter 5 cm attached to a short side. Find the total area (π ≈ 22/7).
Area = rectangle + semicircle.
Radius = 2.5, semicircle = ½π(2.5²).
60 + ½ × (22/7) × 6.25.
≈ 69.82 cm²
2. An L-shaped room is a 9 m by 6 m rectangle with a 3 m by 2 m rectangle removed from a corner. Find its floor area.
Take big rectangle minus the cut.
9 × 6 = 54.
Subtract 3 × 2 = 6.
48 m²
3. A pentagon-shaped sign is a 8 cm by 6 cm rectangle topped by a triangle of base 8 cm and height 3 cm. Find its area.
Split into rectangle + triangle.
Rectangle = 48.
Triangle = ½ × 8 × 3 = 12.
60 cm²
4. A square of side 14 cm has two quarter-circles of radius 7 cm cut from two opposite corners. Find the remaining area (π ≈ 22/7).
Two quarter circles = one half circle.
Square = 196.
Subtract ½ × (22/7) × 49 = 77.
119 cm²
5. A field is a trapezium with parallel sides 20 m and 14 m, height 10 m, plus a triangle of base 14 m and height 6 m attached to the shorter parallel side. Find the total area.
Trapezium = ½(a + b)h.
½(20 + 14)(10) = 170.
Triangle = ½ × 14 × 6 = 42.
212 m²
📝 Topic test — 8 questions
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