# The figure below is the net of a prism made up of identical triangles, what is the total area of the prism if the side of the square is 6 cm.

[a] 75 sq-cm

[b] 84 sq-cm

[c] 95 sq-cm

[d] 56 sq-cm

Last updated date: 25th Mar 2023

•

Total views: 305.7k

•

Views today: 6.83k

Answer

Verified

305.7k+ views

Hint: Find the height of the triangles and use the fact that the area of a triangle $=\dfrac{1}{2}bh$ where b is the base and h is the height and the area of a square $={{a}^{2}}$. There are four triangles and one square. So, the net area will be the sum of 4 times the area of the triangle and area of the square.

Complete step-by-step answer:

Since the length of a side of square = 6cm.

We have AD = 6cm.

Also since the triangles are identical CG = HF

Since the total height of the diagram = 14.

We have CG+AD+HF = 14

i.e. CG+HF+6 = 14

i.e. 2CG+6 = 14

Subtracting 6 from both sides we get

2CG+6-6 = 14-6

i.e. 2CG = 8

Dividing both sides by 2 we get

CG = 4cm

Since CG = HF, we have

HF = 4 cm.

Now we know that the area of a triangle $=\dfrac{1}{2}bh$

Using we get the area of triangle ABC $=\dfrac{1}{2}\times AB\times CG=\dfrac{1}{2}\times 6\times 4=\dfrac{24}{2}=12$

Also, we know that the area of a square $={{a}^{2}}$

Using, we get the area of square ABED $=A{{D}^{2}}={{6}^{2}}=36$.

Hence the total area of the prism = 4 times the area of the triangle ABC + area of square ABED

$=4\times 12+36=48+36=84$

Hence the total area of faces of prism = 84 sq-cm.

Hence option [b] is correct.

Note: Although the figure above is referred to be of a prism, it is a pyramid. A pyramid has triangular faces, whereas a prism has rectangular faces. The diagram above is of a pyramid with a square base.

Further pyramids have only one base, whereas prisms have two.

A cone is an example of a pyramid with a circular base.

Complete step-by-step answer:

Since the length of a side of square = 6cm.

We have AD = 6cm.

Also since the triangles are identical CG = HF

Since the total height of the diagram = 14.

We have CG+AD+HF = 14

i.e. CG+HF+6 = 14

i.e. 2CG+6 = 14

Subtracting 6 from both sides we get

2CG+6-6 = 14-6

i.e. 2CG = 8

Dividing both sides by 2 we get

CG = 4cm

Since CG = HF, we have

HF = 4 cm.

Now we know that the area of a triangle $=\dfrac{1}{2}bh$

Using we get the area of triangle ABC $=\dfrac{1}{2}\times AB\times CG=\dfrac{1}{2}\times 6\times 4=\dfrac{24}{2}=12$

Also, we know that the area of a square $={{a}^{2}}$

Using, we get the area of square ABED $=A{{D}^{2}}={{6}^{2}}=36$.

Hence the total area of the prism = 4 times the area of the triangle ABC + area of square ABED

$=4\times 12+36=48+36=84$

Hence the total area of faces of prism = 84 sq-cm.

Hence option [b] is correct.

Note: Although the figure above is referred to be of a prism, it is a pyramid. A pyramid has triangular faces, whereas a prism has rectangular faces. The diagram above is of a pyramid with a square base.

Further pyramids have only one base, whereas prisms have two.

A cone is an example of a pyramid with a circular base.

Recently Updated Pages

If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE