FIND THE SURFACE AREA OF EACH TRIANGULAR PRISM

Formula for the lateral surface area of the triangular prism,

Lateral surface area = ph

Where,

p = Perimeter of the triangle and h = height of the prism

Formula for the total surface area of the triangular prism,

Total surface area = ph + 2B

Where,

B = Base area of triangular prism

Find the surface area of each triangular prism. Round to the nearest tenth if necessary.

Problem 1 :

Solution :

Lateral surface area = perimeter of base × height

= (25 + 20 + 15) × 10

= 60 × 10

= 600 yd² ---(1)

Area of triangular base = 1/2 × base × height

= 1/2 × 15 × 20

= 150 yd²

2B = 2(150) ==>  300 ---(2)

(1) + (2)

Total Surface area = ph + 2B

= 600 + 300

= 900 yd²

So, total surface area of the triangular prism is 900 yd².

Problem 2 :

Solution :

Lateral surface area = perimeter of base × height

= (24 + 7 + 25) × 18

= 56 × 18

= 1008 km²---(1)

Area of triangular base = 1/2 × base × height

= 1/2 × 24 × 7

= 84 km²

2B = 2(84) ==> 168---(2)

(1) + (2)

Total Surface area = ph + 2B

= (1008 + 168) km²

= 1176 km²

So, total surface area of the triangular prism is 1176 km².

Problem 3 :

Solution :

Lateral surface area = perimeter of base × height

= (17.4 + 10.5 + 1.9) × 14

= 29.8 × 14

= 417.2 ft² ---(1)

Area of triangular base = 1/2 × base × height

= 1/2 × 17.4 × 7

= 60.9

2(60.9) ==> 121.8  ft²---(2)

(1) + (2)

Total Surface area = ph + 2B

= (417.2 + 121.8) ft²

= 539 ft²

So, total surface area of the triangular prism is 539 ft².

Problem 4 :

Solution :

Lateral surface area = perimeter of base × height

= (15.6 + 13 + 13) × 15.6

= 41.6 × 15.6

= 648.96 m² ---(1)

Area of triangular base = 1/2 × base × height

= 1/2 × 15.6 × 10.4

= 81.12

2B = 2(81.12) ==> 162.24 m² ---(2)

(1) + (2)

Total Surface area = ph + 2B

= (648.96 + 162.24) m²

= 811.2 m²

So, total surface area of the triangular prism is 811.2 m².

Problem 5 :

Solution :

Lateral surface area = perimeter of base × height

= (12.75 + 9.25 + 5) × 1.25

= 27 × 1.25

= 33.75 in²  ---(1)

Area of triangular base = 1/2 × base × height

= 1/2 × 12.75 × 3

= 19.125 in²

2B = 2(19.125) ==> 38.25  ---(2)

(1) + (2)

Total Surface area = ph + 2B

= (33.75 + 38.25) in²

= 72 in²

So, total surface area of the triangular prism is 72 in².

Problem 6 :

Solution :

Lateral surface area = perimeter of base × height

= (36 + 30 + 46.8) × 33

= 112.8 × 33

= 3722.4 mm²  -----(1)

Area of triangular base = 1/2 × base × height

= 1/2 × 36 × 30

= 540 mm²

 2B = 2(540) ==>1080 mm²-----(2)

(1) + (2)

Total Surface area = ph + 2B

= (3722.4 + 1080) mm²

= 4802.4 mm²

So, total surface area of the triangular prism is 4802.4 mm².

Problem 7 :

A quart of stain covers 100 square feet. How many quarts should you buy to stain the wheelchair ramp? (Assume you do not have to stain the bottom of the ramp.)

Solution :

Total surface area = 2(Area of triangles) + Area of rectangle

1 ft = 12 inches

1 inch = 1/12 feet

25 inches = 25/12

= 2.08 feet

25  1/2 ft = 301/12 ==> 25.08 ft

= 2 x (1/2) x 25 x 2.08 + 25.08 x 5

= 25 x 2.08 + 25.08 x 5

= 52 + 125.4

= 177.4 square feet

1 quart of stain covers 100 square feet

1 square feet = 1/100 quarts

177.4 square feet = 177.4/100

= 1.774 quarts

Problem 8 :

Work out the surface area of the triangular prism. State the units with your answer.

Solution :

Total surface area = area of two triangles + area of three rectangles

Base of the triangle = 6 cm, height = 8 cm

= 2 x (1/2) x 6 x 8 + (10 x 9) + (9 x 6) + (8 x 9)

= 6 x 8 + 90 + 54 + 72

= 48 + 90 + 54 + 72

= 264 square cm

Problem 9 :

What is the least amount of fabric needed to make the tent?

Solution :

Surface area = area of two rectangles + area of two triangles

= 2(5 x 7) + 2 x (1/2) x 6 x 4

= 70 + 24

= 94 square feet

So, we need 94 square feet of fabric.