**Surface Area**

**Surface Area definition:**The total area of the surface of a three-dimensional object.

----------

**Rectangular Prism:**

*Solution:*

Top:

( length = 5m ; width = 10m )

a =

*l x w*a= 5 x 10

a= 50m

Front:

( length = 6m ; width = 10m )

a=

*l x w*a = 6 x 10

a= 60m

Side:

( length = 6m ; width = 5m )

a=

*l x w*a = 6 x 5

a= 30m

**Total Surface Area Formula:**

TSA = 2( T + F + S)

= 2( 50m + 60m + 30m )

= 2( 140m )

= 280m²

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**Triangular Prism:**

*Solution:*

**Rectangles**

Rectangle 1:

( length

*=*9cm ; width*= 5cm )*a =

*l x w*a = 9 x 5

a = 45cm

^{2}^{}

Rectangle 2:

( length = 10cm ; width = 5cm )

a =

*l x w*a = 10 x 5

a= 50cm²

^{}

( length = 8cm ; width = 5cm )

a = l x w

a = 8 x 5

a = l x w

a = 8 x 5

a = 40m

^{2}^{}

**Triangles**

( base = 8cm ; height = 9cm )

a = b x h

------

2

a = 8 x 9

------

2

*a*= 72

------

2

*a*= 36cm

^{2}

TSA = 50cm + 45cm + 40cm + 36cm + 36cm

= 207cm

^{2}^{}

^{ ----------}

**Cylinder:**

**First Way:**

*Circles:*

r = d

---

2

r = 8mm

-----

2

r = 4mm

*Circumference:*

c = π d

c = 3. 14 x 8

c= 25. 12mm

*Lateral Area:*

*length x width*

25.12 x 12

= 301. 44mm2

*Area of circle*

Area of circle

*=*π r² = 3.14 x 4²

= 3.14 x 16

= 50.24cm²

TSA = 301.44mm + 50.24mm + 50.24mm

=

**401.92mm****²**

**Second Way**

l = 12mm ; d = 8mm

r = d

----

2

r = 8mm

------

2

r = 4mm

^{2}) + (3.14 x 8 x 12)

SA = 2 (π r2)+ (π d h)

SA = 2 (50.24) + (301.44)

SA =

**401.92 mm**^{2}

----------

- Here is a helpful link for a better understanding of Surface Area.
- Here is a helpful video for the formula of a Triangular Prism:

**Volume:**

Triangular Prism:

V = (b x h ÷ 2) x h

V = (3 x 4 ÷ 2) x 8.5

V = 7.5 x 8.5

V = 63.75 m³

V = (3 x 4 ÷ 2) x 8.5

V = 7.5 x 8.5

V = 63.75 m³

Rectangular Prism:

V =

V = 20 x 80 x 16

V = 25600 cm³

*l*x*w*x*h*V = 20 x 80 x 16

V = 25600 cm³

Triangular Prism with fraction:

V = (b x h ÷ 2) x h

V = (8 x 4 ÷ 2) x 6.5

V = 16 x 6.5

V = 104 cm³

V = 16 x 6.5

V = 104 cm³

Cylinder:

r = d ÷ 2

r = 12 ÷ 2

r = 6cm

V = π x r² x h

V = 3.14 x 6² x 15

V = 1695.6 cm³

r = 12 ÷ 2

r = 6cm

V = π x r² x h

V = 3.14 x 6² x 15

V = 1695.6 cm³

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