# Surface Area 3D shapes.

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Surface Area 3D shapes

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3 easy steps to calculate the Surface Area of a solid figure
Determine the number of surfaces and the shape of the surfaces of the solid Apply the relevant formula for the area of each surface Sum the areas of each surface

Surface Area – Basic concept
4 rectangular faces and 2 square faces rectangle rectangle rectangle square square rectangle Determine the number and shape of the surfaces that make up the solid. When you’ve done all that find the area of each face and then find the total of the areas. It might be easier to think of the net of the solid.

Four rectangular faces
Square prism Find the surface area of this figure with square base 5 cm and  height 18 cm Two square faces Four rectangular faces 18 cm 5 cm

Rectangular prism Now sum these areas
Find the surface area of this figure with length 10 cm, width 15 cm and height 12 cm. Now sum these areas 20 cm 15 cm 5 cm

Triangular Prism 1 2 3 Recall
Find the surface area of this figure with dimensions as marked. 12 cm 10 cm 6 8 Use Pythagoras’ theorem to find the  height of the triangle! 12 cm 20 cm 10 cm Hence, total surface area Determine the number of faces and the shape of each face Recall 1 Apply the area formulae for each face 2 Sum the areas to give the total surface area 3

Square Pyramid Find the surface area of this figure with square base 10 cm and  height 12 cm. 12 5 R T 10 Use Pythagoras’ theorem to find the  height of the triangular face. 13 10 13 T R P Each triangular face will have base 10 cm and  height 13 cm. Hence, total surface area 4 triangular faces with the same dimensions and 1 square face 12 We need to find the  height of each triangular face.

First find the unknown heights using Pythagoras’ theorem
Rectangular Pyramid Find the surface area of this figure with dimensions as marked. 10 cm P Q 12 cm 8 cm R S T V 5 faces altogether: 2 pairs of congruent triangular faces 1 rectangular face First find the unknown heights using Pythagoras’ theorem 5 8 89 12 Hence, total surface area 6 8 10

Cylinder h Hence, total surface area
Find the surface area of this cylinder with height 25 cm and diameter 20 cm. Required formula: h 25 cm Curved surface Think of the net of the cylinder to understand the formula. 20 Hence, total surface area

Cone Required formula l refers to the slant height
Find the surface area of this cone of height 15 cm radius 5 cm. Required formula l refers to the slant height l Consider the net of the cone Now calculate the areas. Now sum these areas 5 15 l Use Pythagoras’ theorem Total surface area:

Sphere Required formula
Find the surface area of this sphere with diameter 5 cm. Required formula Easy! The sphere is one continuous surface so just substitute into the formula

Hemisphere Find the surface area of this hemisphere with diameter 5 cm. Total surface area: A hemisphere is a half sphere. But we need to add in the area of the circular base. Required formula

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