Grade 10

Surface area of simple composite solids (no circles)

Lesson

So we know that surface area is the total area of all the faces on a 3D object. We have looked at surface area of prisms.

Sometimes though the shape is a composite solid, (made up of a combination of other solids). These are all composite solids.

To find the surface area of composite solids we need to be able to visualise the different shapes that make up the various surfaces. Once we have identified the different faces and shapes, calculate the areas of each face and add them up separately.

Other common mistakes to be careful about are to not forget faces you may not be able to see in the diagram like those at the back or on the bottom.

Examples

Question 1

In the diagram, the roof has a height of $3$3 metres. Find the surface area of the figure shown,

Round your answer to two decimal places.

A three-dimensional diagram of a composite figure. The structure has a rectangular prism base with dimensions measured $10$ m in length, $5$ m in width, and a height of $6$ m. Attached to the top of the rectangular prism base is a triangular prism, which adds an additional $3$ m to the structure’s height. A dashed line indicates the height of the triangle, perpendicular to the base of the triangle. Each of the slanting sides of the triangular base has a single hash mark.

Question 2

Find the surface area of the figure shown.

Question 3

Find the surface area of the given composite solid.

Outcomes

10P.MT3.04

Solve problems involving the surface areas of prisms, pyramids, and cylinders, and the volumes of prisms, pyramids, cylinders, cones, and spheres, including problems involving combinations of these figures, using the metric system or the imperial system, as appropriate