In this chapter, y'all will revise how to summate the perimeter and expanse of squares, rectangles, triangles and circles. The perimeter of a shape is the distance all the manner around the sides of the shape. The surface area of a shape is the flat space within the shape. You will also larn how to calculate the areas of parallelograms, rhombi, kites and trapeziums, as well as investigate the effect on the perimeter and area of a shape when its dimensions are doubled.

  • Each block in figures A to F below measures 1 cm \(\times\) 1 cm. What is the perimeter and area of each of the figures? Complete the table below.

    The perimeter (P) of a shape is the distance along the sides of the shape. The area (A) of a effigy is the size of the flat surface enclosed by the figure.

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    Figure

    Perimeter

    Surface area

    Number of i cm \(\times\) 1 cm squares

    A

    B

    C

    D

    E

    F

    G

    H
  • Consider the rectangle below. It is formed by tessellating identical squares that are 1 cm by i cm each. The white part has squares that are hidden.

    To tessellate means to cover a surface with identical shapes in such a way that there are no gaps or overlaps. Another discussion for tessellating is tiling.

    1. Write down, without counting, the full number of squares that form this rectangle, including those that are subconscious. Explicate your reasoning.

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    2. What is the area of the rectangle, including the white part?

    Expanse of a rectangle = length \(\times\) latitude = \(l \times b \)

    Surface area of a square = \(l \times 50 = l^{2}\)

    Both length (l) and breadth (b) are expressed in the same unit.

  • Sipho and Theunis each paint a wall to earn some money during the school holidays. Sipho paints a wall 4 m loftier and 10 thousand long. Theunis's wall is 5 thou high and eight 1000 long. Who should be paid more? Explicate.
  • What is the area of a square with a length of 12 mm?
  • The area of a rectangle is 72 cm2 and its length is 8 cm. What is its breadth?
  • The diagram on the left below shows the floor program of a room.
    1. We can calculate the expanse of the room past dividing the floor into two rectangles, as shown in the diagram on the correct beneath.

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      Area of the room = Area of yellow rectangle + Area of red rectangle

      \(= (l \times b) + (l \times b)\\ = (14 \times 9) + (15 \times eight)\\ = 126 + 120\\ = 246 \text{ m}^{2}\)

    2. The yellowish office of the room has a wooden floor and the cherry part is carpeted. What is the area of the wooden floor? What is the area of the carpet?
    3. Calculate the area of the room using two different shapes. Draw a sketch.

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  • Calculate the area of the figures beneath.

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  • Which of the following rules tin be used to summate the perimeter (P) of a rectangle? Explain.
    • Perimeter \(= 2 \times (l + b) \)
    • Perimeter \( = l + b + 50 + b \)
    • Perimeter \( = 2l + 2b \)
    • Perimeter \( = l + b \)

    l and b refer to the length and the latitude of a rectangle.

    The following are equivalent expressions for perimeter:

    \(P = 2l + 2b \) and \(P-2(l + b)\) and \(P = fifty + b +50+b\)

  • Check with ii classmates that the rule or rules you take chosen abover are correct ;and so apply it to summate the perimeter of figure A. Retrieve carefully!
  • The perimeter of a rectangle is 28 cm and its breadth is 6 cm. What is its length?

    • circumference of a circle. You will remember the following aboutcircles from previous grades:

  • The distance across the circle through its centre is called the bore (d) of the circle.
  • The distance from the middle of the circle to any point on the circumference is called the radius (r).
  • The circumference (c) of a circle divided past its diameter is equal to the irrational value we call pi \((\pi)\). To simplify calculations, we often employ the approximate values 3,14 or \(\frac{22}{7}\)

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    • The following are of import formulae to think:

    • \(d = 2 \pi r\) and \(r= \frac{1}{2}d\)
    • Circumference of a circle \((c) = ii \pi r \)
    • Area of a circle \( (A) = \pi r^{2}\)
  • Calculate the perimeter and area of the post-obit circles:
    1. A circle with a radius of five m
    2. A circle with a diameter of 18 mm
  • Calculate the radius of a circumvolve with:
    1. a circumference of 53 cm
    2. a circumference of 206 mm
  • Work out the expanse of the following shapes:

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  • Summate the radius and bore of a circumvolve with:
    1. an area of 200 mii
    2. an area of 1 000 grand2
  • Summate the surface area of the shaded office.

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    • Remember:

    1 cm = 10 mm ane mm = 0,i cm

    1 one thousand = 100 cm 1 cm = 0,01 m

    ane km = 1 000 m one m = 0,001 km

  • Convert the post-obit:
    1. 34 cm = .......... mm
    2. 501 k = .......... km
    3. 226 m = .......... cm
    4. 0,58 km = .......... g
    5. 1,9 cm = .......... mm
    6. 73 mm = .......... cm
    7. 924 mm = .......... 1000
    8. 32,23 km = .......... yard

    • 2 to m2:
    1 cm \(\times\) one cm
    =0.01 g \(\times\) 0.01 k
    =0.0001 yard2 Example:
    Convert 50 cm2to one thousand2
    1 cmtwo = 0,0001 mii
    fifty cmtwo = 50 \(\times\) 0,0001 mtwo
    = 0,005 mii

  • Convert to cm2:
    1. 650 mm2
    2. 1 200 mmii
    3. 18 grandii
    4. 0,045 m2
    5. 93 mm2
    6. 177 chiliad2
    1. Convert 93 mmii to m2
    2. Convert 0,017 km2 to mii

    • 75851.png

    \(\therefore\) Expanse of parallelogram = base \(\times\) perp. superlative

    Nosotros tin use whatever side of the parallelogram as the base, merely we must use the perpendicular superlative on the side we have chosen.

    1. Copy the parallelogram above into your exercise volume.
    2. Using the shorter side as the base of the parallelogram, follow the steps above to derive the formula for the area of a parallelogram.

  • Work out the area of the following parallelograms using the formula.

    Maths_English_term1_p258_1.png

    Maths_English_term1_p258_2.png

    Maths_English_term1_p258_3.png

  • Work out the area of the parallelograms. Use the Theorem of Pythagoras to calculate the unknown sides y'all need. Remember to use the pre-rounded value for meridian and and then circular the concluding answer to two decimal places where necessary.

    Maths_English_term1_p259_1.png

    Maths_English_term1_p259_2.png

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    • Area of a rhomb = length \(\times\) perp. acme

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  • Piece of work in your practise volume. Show how to derive the formula for the area of a rhombus.
  • Calculate the areas of the following rhombi. Circular off answers to two decimal places where necessary.

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    • \(\triangle\)DEG + Area of \(\triangle\)EFG74535.png

    \(\therefore\) Area of a kite = \(\frac{1}{2}\) (diagonal ane \(\times\) diagonal ii)

  • Calculate the surface area of kites with the following diagonals. Give your answers in m2
    1. 150 mm and 200 mm
    2. 25 cm and forty cm
  • Summate the area of the kite.

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    \(\therefore\) Area of a trapezium = \(\frac{1}{2}\) (sum of parallel sides) \(\times\) perp. acme

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  • Calculate the areas of the post-obit 2D shapes. Round off your answers to two decimal places where necessary.
    1. Maths-Gr9-Eng-Term2-p263-img1. png
    2. Maths-Gr9-Eng-Term2-p263-img2. png
    3. Maths-Gr9-Eng-Term2-p263-img3. png
    4. Maths-Gr9-Eng-Term2-p263-img4. png
  • length and breadth for rectangles and squares
  • bases and perpendicular heights for triangles, rhombi and parallelograms
  • two diagonals for kites.

    • Doubling means to multiply by 2.

  • Piece of work out the perimeter and expanse of each shape. Round off your answers to 2 decimal places where necessary.
  • Which effigy in each set is congruent to the original figure?
  • Fill in the perimeter (P) and surface area (A) of each figure in the table below.

    Figure

    Original figure

    Effigy with both dimensions doubled

    A

    P =

    A =

    P =

    A =

    B

    P =

    A =

    P =

    A =

    C

    P =

    A =

    P =

    A =

    D

    P =

    A =

    P =

    A =
  • Wait at the completed table above. What patterns practise you notice? Choose i:
  • When both dimensions of a shape are doubled, its perimeter is doubled and its area is doubled.
  • When both dimensions of a shape are doubled, its perimeter is doubled and its area is four times bigger.

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    1. Write downward the formulae for the post-obit:

      Perimeter of a square

      Perimeter of a rectangle

      Area of a square

      Area of a rectangle

      Surface area of a triangle

      Area of a rhombus

      Area of a kite

      Expanse of a parallelogram

      Area of a trapezium

      Bore of a circle

      Circumference of a circle

      Area of a circle

      1. Calculate the perimeter of the square and the area of the shaded parts of the square.

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      2. Summate the area of the kite.

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