Area Of 3d Figures

Area of 3D Figures

3D Figures  

What are 3D figures? 3D figures are those having three dimensions i.e. X-axis, Y-axis and Z-axis.

Types of 3D Figures.    

Prism Pyramid Cone Cube etc.

PRISM 

A prism is a polyhedron that has two congruent parallel polygons as its bases. The other faces of a prism are parallelograms, most often rectangles. A prism is named for the shape of its base. For instance, this prism is called a perpendicular triangular prism. because two bases are triangular.

PRISM     

Lateral surface area of prism is: Perimeter of base X height of prism surface area= (14+14+14) X 20 = 840 inc2 Total surface area = Lateral surface area+ (2 x (area of base) = Lateral surface area + (2 x ¾ a2) = 840 + (2 x ¾ x 14 x 14) = 840+294 = 1134 inch2

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PYRAMID 

A pyramid is a polyhedron that has only one base. (The base is the "bottom" of the Egyptian pyramids.) The other faces are all congruent triangles, and they share a common vertex, which is the top point. The base can be any type of polygon. If the base is a triangle, then the pyramid has a total of four faces. The Egyptian pyramids have square bases and four triangles as faces.

PYRAMID The area of slanted face of pyramid having square base. = ½ x perimeter of base x slant height = ½ X (4X5) X 3 = 30 cm2 Total area of pyramid = slanted face area + area of base = 30 + 25 = 55 cm2 

CONE 

A cone has a circular base and a vertex that is not on the base. Cones are similar in some ways to pyramids. They both have just one base and they converge to a point, the vertex.

CONE How to calculate height when slant height and radius are given (slant height) 2 = (Height )2 + (radius)2 l2= (h2 + r2) l2 = 82+62 l2 = 64 + 36 l = √100 l = 10 cm 

CONE         

Curved surface area of cone =∏rl = 22/7 x 6 x 10 = 188.4 cm 2 Total surface area of cone = ∏ r (r + l) = 22/7 x 6 (6+10) = 22/7 x 6 x 16 =301.44 cm2

Cube 

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Cube is a box which has 6 equal sides. ‘a’ is the length of the side of each edge of the cube

Cube 

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In words, the surface area of a cube is the area of the six squares that cover it. Area of one square = a2

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So the Surface Area of a Cube = 6 X a

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If a = 3 cm then Surface Area of a Cube = 6 X 3 =6x9 = 54 cm 2

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PRESENTED BY: 

MUKH TAR SING H (MATH MASTER) G.G. Sec. School, Sultanwind Amritsar, PUNJAB