Year 7 Mathematics | Victorian Curriculum 2.0
Length, perimeter, area & circles
Topic 07 | Measurement & Space | Answer key

Year 7 core - answers

Fluency

Length and perimeter

    1. 2.52.5 m
    2. 34003400 m
    3. 8.58.5 cm
    4. 2.52.5 km
    5. 3838 cm
    6. 3636 cm
    7. 2121 cm
    8. 2424 cm
Fluency

Area of rectangles, triangles, parallelograms

    1. 6060 cm^2
    2. 3636 cm^2
    3. 4040 cm^2
    4. 3030 m^2
    5. 5454 cm^2
    6. 66 cm
    7. 88 cm. Method: 12×9×h=36\tfrac{1}{2} \times 9 \times h = 36.
    8. 1212 m. Method: b×5=60b \times 5 = 60.
Fluency

Circles

    1. 88 cm
    2. 99 m
    3. 62.862.8 cm. Method: 2×3.14×102 \times 3.14 \times 10.
    4. 4444 cm. Method: 227×14\tfrac{22}{7} \times 14.
    5. 1010 cm. Method: d=C/π=31.4/3.14d = C / \pi = 31.4 / 3.14.
    6. True - that constant ratio is π\pi.
Reasoning

Explain and reason

    1. Not necessarily. Example: a 4×64 \times 6 rectangle has perimeter 2020 and area 2424; a 2×82 \times 8 rectangle also has perimeter 2020 but area 1616. Same perimeter, different area.
    2. Pete used the slant side, not the perpendicular height. Without the perpendicular height, the area formula cannot be applied directly; more information is needed.
    3. Yes. Example: a thin 1×201 \times 20 rectangle has perimeter 4242 and area 2020, while a 5×55 \times 5 square has perimeter 2020 and area 2525. The first has a larger perimeter but smaller area.
    4. 30+12(π×30)≈30+47.1=77.130 + \tfrac{1}{2}(\pi \times 30) \approx 30 + 47.1 = 77.1 cm. Method: cut across the pizza is 3030 cm; half the circumference is 12πd\tfrac{1}{2}\pi d.
    5. Square wins. Square area =100= 100; rectangle area =96= 96. Among rectangles with the same perimeter (4040 here), the square has the greatest area.
Problem solving

Real-world problems

    1. $4500. Method: perimeter =2(80+45)=250= 2(80 + 45) = 250; cost =250×18= 250 \times 18.
    2. 77 m^2. Method: 12×3.5×4\tfrac{1}{2} \times 3.5 \times 4.
    3. 1111 m. Method: C=πd=227×3.5=11C = \pi d = \tfrac{22}{7} \times 3.5 = 11.
    4. 960 000960\,000 cm^2. Method: 9696 m^2; 11 m^2 =10 000= 10\,000 cm^2.
    5. 4444 m (to nearest metre). Method: C=227×70=220C = \tfrac{22}{7} \times 70 = 220 cm per turn =2.2= 2.2 m; ×20=44\times 20 = 44 m.

Extension - answers

Reasoning

Trapezium and composite areas

    1. 2121 cm^2. Method: 12(4+10)×3=21\tfrac{1}{2}(4 + 10) \times 3 = 21.
    2. 3232 m^2. Method: 12(6+10)×4=32\tfrac{1}{2}(6 + 10) \times 4 = 32.
    3. 3434 m^2. Method: 40−640 - 6.
    4. 3636 m^2. Method: outer 12×8=9612 \times 8 = 96; garden 10×6=6010 \times 6 = 60; path =96−60= 96 - 60.
    5. 11001100 cm^2. Method: 40×30−4×52=1200−10040 \times 30 - 4 \times 5^2 = 1200 - 100.
Year 7 Mathematics study companion | Answer key