Area of composite shapes

To calculate the area of a composite shape you must divide the shape into rectangles, triangles or other shapes you can find the area of and then add the areas back together.

You may have to calculate missing lengths before finding the area of some of the shapes.

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Area of a compound shape
Calculate the area of this compound shape.
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Area of a compound shape
Divide the shape into rectangles and triangles and label each one.
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Area of a compound shape
Rectangle A: first calculate the length of the rectangle. The total length of the shape is 12 cm, subtract 4 cm and 1 cm = 7 cm.
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Area of a compound shape
Area of rectangle A = length × width = 10 × 7 = 70 cm^{2}.
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Area of a compound shape
Rectangle B: first calculate the length of the rectangle. The length of rectangle B = 4 cm + 1 cm = 5 cm.
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Area of a compound shape
Area of rectangle B = length × width = 5 × 4 = 20 ^{2}
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Area of a compound shape
Triangle C: first calculate the height of the triangle. Total height of the shape is 10 cm. Subtracting the 4 cm length of the square which the triangle is sitting on leaves 6 cm for the height of the triangle.
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Area of a compound shape
Area of triangle C = ½ × base × height = ½ × 1 × 6 = ^{2}
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Area of a compound shape
Add up the areas of all the shapes. Total area = A + B + C = 70 + 20 + 3 = 93 ^{2}

Other composite shapes may have cut out sections. To work out the area of these shapes, you must calculate the area of the main shape and subtract the area of the cut-out.

Question

Calculate the area of the shaded shape.

A rectangle of width 20 mm and height 15 mm. Inside the rectangle is a cut-out section in the shape of a trapezium

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