SURFACE AREA OF SURFACE AREA OF SOLIDSSOLIDS

By: SAMUEL M. GIERBy: SAMUEL M. GIER

WHAT’S A SPACE FIGURE?WHAT’S A SPACE FIGURE?

-any figure that is three –dimensional is a space figure.

NOTE: All solids are three-dimensional

THE COMMON SOLIDSTHE COMMON SOLIDS

A. PRISM * SQUARE

PRISM *RECTANGULAR

PRISM * TRIANGULAR

PRISM * CUBE

B. PYRAMIDS * SQUARE

PYRAMIDS * TRIANGULAR

PYRAMIDS * RECTANGULAR

PYRAMIDS

A. POLYHEDRON

COMMON SOLIDSCOMMON SOLIDSCYLINDERSCYLINDERS

COMMON SOLIDSCOMMON SOLIDS

REFLECTIVE TRAFFIC CONE

COMMON SOLIDSCOMMON SOLIDSSPHERESSPHERES

THE EARTHBALLS

SURFACE AREA SURFACE AREA OF SOLIDSOF SOLIDS

SURFACE AREA or total area

The sum of the areas of the outer surfaces( FACES) of a solid.

Every solid figure has a surface area.

SURFACE AREA OF PRISMSSURFACE AREA OF PRISMS

-is a polyhedron whose bases are congruent and parallel polygons.

Base

Base

Lateral face

The faces of a prism which are not its bases are called LATERAL FACES.

SURFACE AREA OF A CUBESURFACE AREA OF A CUBE

Base

Lateral face

The faces of a CUBE are SQUARES and are equal to its BASES.

To find the surface area of a CUBE, multiply the SQUARE of the length of a side by 6.

The surface area of a CUBE with side sSA = 6s².

Note:There are 6 faces of a cube.2 bases and 4 lateralFaces.

EXAMPLE 1EXAMPLE 1

5 cm

5 cm

Find the surface area of a cube, the lateral faces of which are bounded by a length of 5 cm.

Solution:SA = 6s². = 6(5cm) ² = 6(25 cm²) SA= 150 cm²

EXAMPLE 2EXAMPLE 2

10 cm

10 cm

Find the surface area of a cube, the lateral faces of which are bounded by a length of 10 cm.

Solution:SA = 6s². = 6(10cm) ² = 6(100 cm²) SA= 600 cm²

SURFACE AREA OF A SQUARE SURFACE AREA OF A SQUARE PRISMPRISM

Base

Lateral face

The Lateral faces of a SQUARE PRISM are RECTANGLES. The bases are SQUARES.

To find the surface area of a SQUARE PRISM, add the area of the bases and the areas of its lateral faces.

Note:There are 6 faces of a square prism.2 bases and 4 lateralFaces.

Height (h)

SURFACE AREA OF A SQUARE SURFACE AREA OF A SQUARE PRISMPRISM

Base

Lateral face

Height (h)

The surface area of a SQUARE PRISM with BASE side s and HEIGHT h, SA = 2s² + 4 sh.

Note:A square prism has2 bases and 4 lateralFaces.

ss

h

FIND THE SURFACE AREA OF A FIND THE SURFACE AREA OF A SQUARE PRISM SHOWN BELOW.SQUARE PRISM SHOWN BELOW.

Solution:SA = 2s² + 4 shSA = 2(3 cm)² + 4 (3cm)(8 cm)

SA = 2(9 cm²) + 4 (24 cm²)SA = 18 cm² + 96 cm²SA = 114 cm²

3 cm3 cm

8 cm

Given: s = 3 cm, h= 8 cmGiven: s = 3 cm, h= 8 cm

FIND THE SURFACE AREA OF A FIND THE SURFACE AREA OF A SQUARE PRISM SHOWN BELOW.SQUARE PRISM SHOWN BELOW.

Solution:SA = 2s² + 4 shSA = 2(2 cm)² + 4 (2cm)(6 cm)

SA = 2(4 cm²) + 4 (12 cm²)SA = 8 cm² + 48 cm²SA = 56 cm²

2 cm2 cm

6 cm

Given: s = 2 cm, h= 6 cmGiven: s = 2 cm, h= 6 cm

Find the surface area of the following solids.

1. a cube with s = 2.2 cm.2. a square prism with s =

12 cm and h= 14 cm.

ASSIGNMENTSASSIGNMENTS

1.Which among the solids has only one vertex?2.Which among the solids has congruent

circular bases?3.Which among the solids are bounded

by a regular polygon?