Composite solids - Intermediate and Higher tier - Surface area and volume - WJEC - GCSE Maths Numeracy (WJEC) Revision

Composite solids - Intermediate and Higher tier

When calculating the volume or surface area of a composite solid, split the shape up into sections and calculate each element separately.

Calculate the volume of the model house.

Image caption,
Surface area of a composite shape
To calculate the surface area of this shape, start by identifying the dimensions of each surface.
Image caption,
Surface area of a composite shape
The front face and the back face are identical. Once we have calculated the area of one, we can double it.
Image caption,
Surface area of a composite shape
Split the L shape into two rectangles and add together the areas: Area = 5 × 11 + 15 × 4 = 55 + 60 = 115 cm squared, Area of front and back = 2 × 115 = 230 cm squared.
Image caption,
Surface area of a composite shape
The area of the bottom face is equal to the two sections on the top of the shape.
Image caption,
Surface area of a composite shape
Area = 6 × 20 = 120 cm squared, Area of the top and bottom = 2 × 120 = 240 cm squared.
Image caption,
Surface area of a composite shape
The area on the left hand side of the shape is equal to the two shaded regions on the right hand side.
Image caption,
Surface area of a composite shape
Area = 11 × 6 = 66 cm squared, Area of left and right = 2 × 66 = 132 cm squared.
Image caption,
Surface area of a composite shape
The total surface area = 230 + 240 + 132 = 602 cm squared.