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3 For each of the statements below select the option that is true by writing the LETTER that corresponds to the correct answer in the space provided.

Mathematics

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3 parts
12.1

A=πr2A = \pi r^2

12.2

A=12×base×heightA = \frac{1}{2} \times \text{base} \times \text{height}

12.3

π\pi

Step-by-step solution

3 steps

Part 11.3

Part a

Shape has 2 pairs of parallel sides and corners of 90∘90^\circ.

The shape described is a square.

  • A

Part b

Shape has 1 pair of parallel sides.

The shape described is a trapezium.

  • D

Part c

Shape has one pair of opposite angles equal.

The shape described is a kite.

  • C

Part d

Only one diagonal is bisected.

The shape described is a kite.

  • C

Part e

All four sides are equal.

The shape described is a square.

  • A

Part 12

Part 12.1

A=πr2A = \pi r^2

Write down the formula for the area of a circle.

The formula for the area of a circle is:

A=πr2A = \pi r^2

Where AA is the area and rr is the radius.

  • A=πr2\boxed{A = \pi r^2}

Part 12.2

A=12×base×heightA = \frac{1}{2} \times \text{base} \times \text{height}

Write down the formula for the area of a triangle.

The formula for the area of a triangle is:

A=12×base×heightA = \frac{1}{2} \times \text{base} \times \text{height}

Where AA is the area, 'base' is the length of the base, and 'height' is the perpendicular height.

  • A=12×base×height\boxed{A = \frac{1}{2} \times \text{base} \times \text{height}}

Part 12.3

π\pi

What is the value of circumference2×radius\frac{\text{circumference}}{2 \times \text{radius}}?

  1. Write down the formula for the circumference of a circle.

    The circumference CC of a circle with radius rr is given by:

    C=2πrC = 2 \pi r

  2. Substitute the circumference formula into the given expression.

    circumference2×radius=2πr2r\frac{\text{circumference}}{2 \times \text{radius}} = \frac{2 \pi r}{2 r}

  3. Simplify the expression.

    2πr2r=π\frac{2 \pi r}{2 r} = \pi
    • π\boxed{\pi}
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