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Area of polygons Questions

1.  The figure below is a squre based pyramid ABCD with AB = BC = 6cm and height VO = 10cm.

Image From EcoleBooks.com

 

 (a) State the projection of VA on the base ABCD. (1mk)

 (b) Find the length VA. (3mks)

 (c) Calculate angle between VA and plane ABCD. (2mks)

 (d) Find angle between VCD and ABCD.  (2mks)

 (e) Calculate the volume of the solid (2mks)

2.  The diagram below, not drawn to scale, is a regular pentagon circumscribed in a circle of radius 10 cm at centre O

 

 

 

 

 

 

ecolebooks.com

 

 

 

 

 

 

 

 

 

 

 

Find

(a) The side of the pentagon (2 mks)

(b) The area of the shaded region (3 mks)

3.  PQRS is a trapezium in which PQ is parallel to SR, PQ = 6cm, SR = 12cm, Image From EcoleBooks.comPSR = 400 and PS = 10cm. Calculate the area of the trapezium. (4mks)

 

 

 

 

 

 

 

 

4.  A regular octagon has an area of 101.8 cm2. calculate the length of one side of the octagon (4marks)

5.  Find the area of a regular polygon of length 10 cm and side n, given that the sum of interior

angles of n : n –1 is in the ratio 4 : 3.

6.  Calculate the area of the quadrilateral ABCD shown:-

 

 

 

 

 

 

 

 

 

Area of polygons Answers

1.

(a) AC

(b) AC = Image From EcoleBooks.com

= Image From EcoleBooks.com

= 8.485

Image From EcoleBooks.com ½ x 8.485 = 4.243

VA = Image From EcoleBooks.com

= Image From EcoleBooks.com

= 10.863.

(c)

Image From EcoleBooks.com

Cos  = Image From EcoleBooks.com

Cos  = 0.39059

 = 67.010

(d)

Image From EcoleBooks.com

Tan  = 10/3

 = 73.300

 

(e) Vol = 1/3 x 6 x 6 x 10

= 120cm3

B1

 

 

M1

 

 

 

M1

 

A1

 

 

 

 

 

 

 

 

M1

 

A1

 

 

 

 

 

 

 

 

M1

A1

 

M1

A1

 
  

10

 

 

 

 

 

 

1.  180( n – 2) = 4

 180 (n -1 – 2) 3

  540n – 1080 = 720n – 2160

 720n – 540n – 2160 – 1080

  180n = 1080

n = 6

 Area of hexagon = 6 ( ½ x 10 x sin 60)

 = 6 x 43.30 = 259.81 cm2

2.  

 

 

 

 

 

 

 

 

Area rt  = ½ x 8 x 6

S = 12 + 14 + 10

 2

A = 18(18-12) (18-14) (18-10)

= 18 x6 x 4 x 8

= 3456

= 58. 79

Total area = 24 + 58. 79 = 82.79


 




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