Surface Area Of Composite Shapes

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Perimeter and area - WJEC

Knowing how to find the perimeter or area of a shape can be useful in everyday life - from wrapping a present to buying a rug. Apply it in calculations to find the amount of materials needed or price.

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Surface area of composite shapes

To calculate the expanse of a composite shape you must divide the shape into rectangles, triangles or other shapes y'all tin detect the area of and and so add the areas back together.

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

A composite shape with sides of various lengths. The lengths of four of the sides are unknown

Area of a chemical compound shape

Calculate the surface area of this compound shape.

A composite shape. The shape has been divided into two rectangles, labelled 'A' and 'B', and a triangle, labelled 'C'

Area of a compound shape

Divide the shape into rectangles and triangles and characterization each one.

A composite shape. The shape has been divided into two rectangles, labelled 'A' and 'B', and a triangle, labelled 'C'. The height of rectangle A is 10 cm, the width is unknown

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 one cm = vii cm.

Rectangle A with height equal to 10 cm, and width equal to 7 cm

Area of a compound shape

Area of rectangle A = length × width = 10 × 7 = 70 cm squared.

A composite shape. The shape has been divided into two rectangles, labelled 'A' and 'B', and a triangle, labelled 'C'. The height of rectangle B is 4 cm, the width is unknown

Area of a compound shape

Rectangle B: showtime calculate the length of the rectangle. The length of rectangle B = 4 cm + 1 cm = 5 cm.

Rectangle B with width equal to 5 cm, and height equal to 4 cm

Area of a compound shape

Area of rectangle B = length × width = 5 × 4 = 20 cm squared

A composite shape. The shape has been divided into two rectangles, labelled 'A' and 'B', and a triangle, labelled 'C'. The base of triangle C is 1 cm, the height is unknown

Area of a compound shape

Triangle C: first calculate the height of the triangle. Full peak of the shape is ten cm. Subtracting the iv cm length of the foursquare which the triangle is sitting on leaves half dozen cm for the summit of the triangle.

Triangle C with base equal to 1 cm, and height equal to 6 cm

Area of a compound shape

Expanse of triangle C = ½ × base × meridian = ½ × 1 × 6 = iii cm squared.

A composite shape divided into two rectangles, labelled 'A' and 'B', and a triangle, labelled 'C'. Rectangle A is 70 cm squared, rectangle B is 20 cm squared, and the triangle is 3 cm squared

Area of a compound shape

Add upwards the areas of all the shapes. Full area = A + B + C = seventy + xx + three = 93 cm squared.

Other blended shapes may have cut out sections. To piece of work out the area of these shapes, y'all must calculate the area of the master shape and subtract the area of the cut-out.

Question

Calculate the expanse 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

Area of the rectangle = 15 × xx = 300 mm ⁱⁱ
Expanse of the trapezium = ½ × (10 + xiii) × 6 = ½ × 23 × 6 = ½ × 138 = 69 mm ⁱⁱ
Area of the shaded shape = 300 – 69 = 231 mm ^two