SURFACE AREA OF 3D SHAPES WORKSHEET

Surface area of 3d shapes worksheet :

Surface area of 3d shapes worksheet is much useful to the students who would like to practice problems on 3-D shapes such as cubes, cuboids, prisms and pyramids.

Surface area of 3d shapes worksheet - Problems

1)  Find the surface area of the cuboid given below.

2)  Find the surface area of the cube given below.

3)  Find the surface area of the triangular prism given below.

4)  Find the surface area of the triangular prism given below.

5)  Find the surface area of the triangular prism given below.

6)  Find the surface area of the pyramid given below.

7)  Find the surface area of the pyramid given below.

8)  Find the surface area of the pyramid given below.

Surface area of 3d shapes -Answers

Problem 1 : 

Find the surface area of the cuboid given below.

Solution : 

Surface area of cuboid   =  Sum of areas of all six faces

In cuboid, each face is a rectangle. So we can use area of rectangle formula to get area of each face. 

Area of the front face  =  8 x 12  =  96 sq. cm   

Area of the back face  =  8 x 12  =  96 sq.cm

Area of the left side face  =  4 x 8  =  32 sq.cm 

Area of the right side face  =  4 x 8  =  32 sq.cm

Area of the top portion  =  4 x 12  =  48 sq.cm

Area of the base  =  4 x 12  =  48 sq. cm

Surface area of cuboid   =  Sum of areas of all six faces

Surface area of cuboid   =  96 + 96 + 32 + 32 + 48 + 48

Surface area of cuboid   =  96 + 96 + 32 + 32 + 48 + 48

Surface area of cuboid   =  352 sq. cm

Alternative method : 

We can use the formula given below to find surface area of cuboid.

Surface area of cuboid  =  2(lh + wh + lw) 

Here, l  =  12 cm, w  =  4 cm and h  =  8 cm.

Surface area of cuboid  =  2(12x8 + 4x8 + 12x4) 

Surface area of cuboid  =  2(96 + 32 + 48)

Surface area of cuboid  =  2(176)

Surface area of cuboid  =  352 sq.cm

Problem 2 : 

Find the surface area of the cube given below.

Solution :

We know that the shape of each face of a cube is a square.

In the above cube, the side length of each face is "8". 

So, area of each face (square)  =  8 x 8  =  64 sq.cm

Therefore,

surface area of the cube  =  6 x area of each face 

surface area of the cube  =  6 x 64 

Surface area of the cube  =  384  sq.cm

Problem 3 : 

Find the surface area of the triangular prism given below.

Solution :

In the above triangular prism, there are five faces. The shape of the base, vertical face and slanting face is rectangle. The shape of two faces on the left side and right side is triangle.

For the given triangular prism, 

Area of the base  =  7 x 4  =  28 sq.cm 

Area of the vertical face  =  3 x 7  = 21 sq.cm

Area of the slanting face  =  5 x 7  =  35 sq. cm

Area of the front face  =  (1/2) x 4 x 3  =  6 sq.cm

Area of the back face  =  (1/2) x 4 x 3  =  6 sq.cm

So,

surface area  =  sum of the area of 5 faces

surface area  =  28 + 21 + 35 + 6 + 6

Surface area of the triangular prism  =  96 sq.cm

Problem 4 : 

Find the surface area of the triangular prism given below.

In the above triangular prism, there are five faces. The shape of the base and the two slanting faces is rectangle. The shape of two faces on the left side and right side  is triangle. 

For the given triangular prism, 

Area of the base  =  8 x 12  =  96 sq.cm 

Area of the first slanting face  =  12 x 5  = 60 sq.cm

Area of the other slanting face  =  12 x 5  =  60 sq. cm

Area of the front face  =  (1/2) x 8 x 3  =  12 sq.cm

Area of the back face  =  (1/2) x 8 x 3  =  12 sq.cm

So,

surface area  =  sum of the area of 5 faces

surface area  =  96 + 60 + 60 + 12 + 12

Surface area of the triangular prism  =  240 sq.cm

Problem 5 : 

Find the surface area of the triangular prism given below.

In the above triangular prism, there are five faces. The shape of the base and top portion is triangle. The shape of the faces being as side walls of the prism is rectangle. 

For the given triangular prism, 

Area of the base  =  (1/2) x 6 x 4  =  12 sq.cm 

Area of the top portion  =  (1/2) x 6 x 4  =  12 sq.cm

Area of the front face (rectangle)  =  6 x 8  =  48 sq.cm

Area of the first back face (rectangle)  =  8 x 5  =  40 sq.cm

Area of the other back face (rectangle)  =  8 x 3  =  24 sq.cm

So,

surface area  =  sum of the area of 5 faces

surface area  =  12 + 12 + 48 + 40 + 24

Surface area of the triangular prism  =  136 sq.cm

Problem 6 : 

Find the surface area of the pyramid given below.

Solution : 

Surface area of the pyramid   =  Sum of areas of all 5 faces

In the above pyramid, the base is a square with side length 5 cm and each wall is a triangle with base 5 cm and height 8 cm.

Let us find the area of each face separately. 

Area of the base  =  5 x 5  =  25 sq.cm

Area of each side wall  =  (1/2) x 5 x 8  =  20 sq.cm 

Area of all 4 side walls  =  4 x 20  =  80 sq.cm 

Surface area of the above pyramid  =  25 + 80

Surface area of the above pyramid  =  105 sq.cm

Problem 7 : 

Find the surface area of the pyramid given below.

Solution : 

Surface area of the pyramid   =  Sum of areas of all 4 faces

In the above pyramid, the base is an equilateral triangle with side length 4 cm and each wall is a triangle with base 4 cm and height 6 cm.

Let us find the area of each face separately. 

Area of the base  =  (√3/4) x 4²  =  4√3 sq.cm

Area of each side wall  =  (1/2) x 4 x 6  =  12 sq.cm 

Area of all 3 side walls  =  3 x 12  =  36 sq.cm 

Surface area of the above pyramid  =  (4√3 + 36)  sq.cm

Surface area of the above pyramid  =  4(√3 + 9)  sq.cm

Problem 8 : 

Find the surface area of the pyramid given below.

Solution : 

Surface area of the pyramid   =  Sum of areas of all 4 faces

In the above pyramid, the base is an equilateral triangle with side length 4 cm and each wall is a triangle with base 4 cm and height 6 cm.

Let us find the area of each face separately. 

Area of the base  =  (√3/4) x 6²  =  9√3 sq.cm

Area of each side wall  =  (1/2) x 6 x 10  =  30 sq.cm 

Area of all 3 side walls  =  3 x 30  =  90 sq.cm 

Surface area of the above pyramid  =  (9√3 + 90)  sq.cm

Surface area of the above pyramid  =  9(√3 + 10)  sq.cm

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