**Prism**is a polyhedron with an n-sided polygonal base, another congruent parallel base (with the same rotational orientation), and n other faces (necessarily all parallelograms) joining corresponding sides of the two bases. All cross-sections parallel to the base faces are congruent to the bases. (

*from Wikipedia*)

A **Pyramid** is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a lateral face. It is a conic solid with polygonal base (*from Wikipedia*)

A **Tetrahedron** is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedron and the only one that has fewer than 5 faces.(*from Wikipedia*)

– **Height (h) = (√2)/(√3) * (Side)****Total Surface Area (TSA) = (3√3)/4 * (Side) ^{2}**

**Lateral Surface Area (LSA) = (4√3)/4 * (Side)**

^{2}**Volume (V) = (√2)/12 * (Side)**

^{3}#### Questions for Practice:

__Since, triangle ABC is__

**Ans:***scalene triangle*.

**Perimeter**(P) = 5+8+7 =

**20cm**

The

**area of ABC = √10*(10-5)*(10-8)*(10-7) = √(10*5*2*3) = 10√3.**

**LSA** = Perimeter * Altitude = 20 * 9 = **108 cm ^{2}**

**TSA** = LSA + 2 x Area of ABC = **108+20√3 cm ^{2}**

**Volume** = Area x altitude = 10√3 * 9 = **90√3 cm ^{3}**

^{3}. Find the Height (H)?**Ans:**

**Ans: **

**Ans:****Lateral Surface area** = 144√3 = √3 * side^{2}

=> side^{2} = 144 => side = 12 cm.

=> **TSA** = 3√3/4 * side^{2} = 3√3/4 * 12^{2} = 27√3 cm^{2}.

=> **Volume** = √2/12 * side^{3} = √2/12 * 12^{3} = 144V2

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