Surface area of prism and pyramid worksheet is much useful to the students who would like to practice problems on 3D shapes.

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 pyramid given below.

7) Find the surface area of pyramid given below.

8) Find the surface area of pyramid given below.

**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**

Let us look at the next problem on "Surface area of prism and pyramid worksheet"

**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**

Let us look at the next problem on "Surface area of prism and pyramid worksheet"

**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**

Let us look at the next problem on "Surface area of prism and pyramid worksheet"

**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**

Let us look at the next problem on "Surface area of prism and pyramid worksheet"

**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**

Let us look at the next problem on "Surface area of prism and pyramid worksheet"

**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**

Let us look at the next problem on "Surface area of prism and pyramid worksheet"

**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**

Let us look at the next problem on "Surface area of prism and pyramid worksheet"

**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**

After having gone through the stuff given above, we hope that the students would have understood "Surface area of prism and pyramid worksheet".

Apart from the stuff given above, if you want to know more about "Surface area of prism and pyramid worksheet", please click here

Apart from the stuff, "Surface area of prism and pyramid worksheet", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**