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.