FIND LATERAL AND TOTAL SURFACE AREA OF RECTANGULAR PRISM

In geometry, a rectangular prism can be defined as a 3-dimensional solid shape which has six faces that are rectangles. A rectangular prism is also a cuboid.

What is lateral surface area ?

The lateral surface of an object is all of the sides of the object, excluding its base and top. The lateral surface area is the area of the lateral surface.

What is total surface area ?

The total surface of an object is all of the sides of the object, including its base and top. 

Lateral surface area of rectangular prism = 2h(l + w)

Total surface area of rectangular prism = 2(lw + wh + hl)

Find the 

(i) Lateral surface area and 

(ii)  Total surface area of the following rectangular prism.

Problem 1 :

Solution :

From the prism,

l = 5 cm, w = 1 cm and h = 2 cm

(i) Lateral surface area = 2h (l +w)

= 2(2)(5 + 1)

= 4(6)

= 24 cm²

(ii) Total surface area of the rectangular prism

= 2(lw + lh + wh)

= 2 [(5 × 1) + (5 × 2) + (1 × 2)]

= 2(5 + 10 + 2)

= 2(17)

= 34 cm²

Problem 2 :

Solution :

From the prism,

l = 10 ft, w = 2 ft and h = 5 ft

(i) Lateral surface area = 2h (l +w)

= 2(5)(10 + 2)

= 10(12)

= 120 ft²

(ii)  Total surface area of the rectangular prism

= 2(lw + lh + wh)

= 2 [(10 × 2) + (10 × 5) + (2 × 5)]

= 2(20 + 50 + 10)

= 2(80)

= 160 ft²

Problem 3 :

Solution :

From the prism,

l = 6 m, w = 3 m and h = 1 m

(i) Lateral surface area = 2h (l +w)

= 2(1)(6 + 3)

= 2(9)

= 18 m²

(ii)  Total surface area of the rectangular prism

= 2(lw + lh + wh)

= 2 [(3 × 1) + (3 × 6) + (1 × 6)]

= 2(3 + 18 + 6)

= 2(27)

= 54 m²

Problem 4 :

Solution :

From the prism,

l = 10 in, w = 11/2 in and h = 25/4 in

(i) Lateral surface area = 2h (l + w)

= 2(25/4)(10 + 11/2)

= (25/2)(31/2)

= 193.75 ft²

(ii)  Total surface area of the rectangular prism

= 2(lw + lh + wh)

= 2 [(11/2 × 10) + (25/4 × 11/2) + (10 × 25/4)]

= 2(55 + 34.375 + 62.5)

= 2(151.87)

= 303.75 ft²

Problem 5 : 

Solution :

From the prism,

l = 5.5 yd in, w = 2.8 yd and h = 5.5 yd

(i) Lateral surface area = 2h (l + w)

= 2(5.5)(5.5 + 2.8)

= 11(8.3)

= 91.3 yd²

(ii)  Total surface area of the rectangular prism

= 2(lw + lh + wh)

= 2 [(5.5 × 2.8) + (5.5 × 5.5) + (2.8 × 5.5)]

= 2(15.4+ 30.25 + 15.4)

= 2(61.05)

= 122.1 yd²