Answer
Verified
423.9k+ 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
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What organs are located on the left side of your body class 11 biology CBSE
Write an application to the principal requesting five class 10 english CBSE
What is the type of food and mode of feeding of the class 11 biology CBSE
Name 10 Living and Non living things class 9 biology CBSE