Area & perimeter of composite figures - Wiki

  • #area
    • The figure shows a circle inside a square. Find the area of the unshaded part. (Take `pi = 22/7`)
      • #area&perimeterofcompositefigures

        Area of square

        14 `xx` 14 = 196 cm2

        Radius of circle

        14 `-:` 2 = 7 cm

        Area of circle

        `22/7` `xx` 7 `xx` 7 = 154 cm2

        Area of unshaded part

        196 - 154 = 42 cm2  

         

    • The figure below is made up of a quadrant and a rectangle, OPQR. Find the perimeter of rectangle OPQR. Ans: _BLANK_ cm
      • #area&perimeterofcompositefigures

        Length of rectangle

        8 - 1 = 7 cm

        perimeter of rectangle

        5 + 7 + 5 + 7 = 24cm

    • A swimming pool takes the shape of 2 semi-circles and a rectangle shown below. Andy walked 15 rounds along the perimeter of the swimming pool. What was the total distance Andy walked? Give your answer in kilometres. (Take `pi = 3.14`) Ans: _BLANK_ km [3]
      • #area&perimeterofcompositefigures

        Perimeter of the swimming pool

        25 + 25 + ( `Pi` `xx` D )

        50 + (3.14 `xx` 10)

        50 + 31.4 = 81.4 m

        Total distance travel

        81.4 `xx` 15 = 1221 m

        1221 m = 1.221 km 

    • The table mat below is made up of identical semi-circles and a 31-cm square. a) Find the perimeter of the entire table mat. b) Half of the table mat is shaded. Find the area of the shaded part. (Take `pi = 22/7`) Ans: a) _BLANK_ cm [2] Ans: b) _BLANK_ cm`^2` [3]
      • #area&perimeterofcompositefigures

        (part a):

        The 8 semi-circles made uo 4 full circles

        Diameter of 1 semi-circle

        (31 - 17)`-:` 2 = 14 `-:` 2 = 7 cm

        Circumference of 1 semi-circle

        `22/7`  `xx` 7  = 22 cm

        Circumference of 4 semi - circles

        22 `xx` 4 = 88 cm

        Perimeter of circles

        88 + (17`xx` 4) = 156 cm

        (part b):

        Area of half square

        31 `xx` 31 `xx` `1/2`  = 480.5 cm2

        Radius of semi- circle

        `-:` 2 = 3.5 cm

        Area of 2 circles

        `xx` `22/7`  `xx` 3.5 `xx` 3.5 = 77 cm2

        Area of shaded area

        480.5 + 77 = 557.5 cm2        

          

          

         

    • The figure below is formed by a square AOBC and a circle with centre O. AOB is part of the circle. The length of AO is 7 cm. Find the perimeter of the figure. (Take `pi = 22/7`)
      • #area&perimeterofcompositefigures

        Total perimeter of the figure is  `3/4`  of the circumference of the circle plus two sides of the square AOBC

        Radius = 7 cm

        Diameter = 7 `xx` 2 = 14 cm

        Circumference

        `3/4`  `xx` `22/7`  `xx` 14 = 33 cm

        Total perimeter

        33 + 7 + 7 = 47 cm