Math – Grade 6 Unit 3 Measurement: Shape and Space

Surface Area

SO 4,5 By Vernon Savoury

Definition

• Surface Area – is the total number of unit squares used to cover a 3-D surface.

Find the SA of a Rectangular Solid

Top A rectangular solid has 6 faces.

They are: Front Right Side Top Bottom Front Back Right Side Left Side We can only see 3 faces at any one time.

Which of the 6 sides are the same?

Top and Bottom Front and Back Right Side and Left Side

Surface Area of a Rectangular Solid

Top Front Right Side

We know that

Each face is a rectangle.

and the

Formula for finding the area of a rectangle is: A = lw Steps: Find: Area of Top Area of Front Area of Right Side Find the sum of the areas Multiply the sum by 2.

The answer you get is the surface area of the rectangular solid.

Find the Surface Area of the following: Find the Area of each face: 12 m Top 5 m A = 12 m x 5 m = 60 m 2 Top Right Side 8 m Front Front 8 m A = 12 m x 8 m = 96 m 2 5 m 12 m 12 m Sum = 60 m 2 + 96 m 2 + 40 m 2 = 196 m 2 Multiply sum by 2 = 196 m 2 x 2 = 392 m 2 Right Side 8 m A = 8 m x 5 m = 40 m 2 5 m The surface area = 392 m 2

14 cm 84 m 2 6 cm 24 m 2 56 m 2 Find the Surface Area 4 cm Area of Top = 6 cm x 4 cm = 24 cm 2 Area of Front = 14 cm x 6 cm = 84 cm 2 Area of Right Side = 14 cm x 4 cm = 56 cm 2 Find the sum of the areas: 24 cm 2 + 84 cm 2 + 56 cm 2 = 164 cm 2 Multiply the sum by 2: 164 cm 2 x 2 = 328 cm 2 The surface area of this rectangular solid is 328 cm 2 .

Nets

• A net is all the surfaces of a rectangular solid laid out flat.

Back 8 cm 8 cm Top Front Right Side 5 cm 10 cm Left Side Top Front Right Side 5 cm 8 cm 8 cm Bottom 10 cm 5 cm

Find the Surface Area using nets .

Top Right Side Front 8 cm 5 cm 10 cm Each surface is a rectangle.

A = lw Find the area of each surface.

Which surfaces are the same?

Find the Total Surface Area.

Left Side 80 80 Back Top Front What is the Surface Area of the Rectangular solid?

340 cm 2 8 cm Right Side 8 cm 5 cm 8 cm Bottom 10 cm 50 50 5 cm 40 40