Question

1. work out the area of this composite shape:

1. calculate the area of this circle.

radius = 15 cm
(round to 2 decimal places)

1. a circular plate has a diameter of 28 cm.

find its circumference.
(round to 2 decimal places)

1. find the volume of this cuboid:

length = 9 cm
width = 4 cm
height = 6 cm

section c: geometry - angle rules
write the reasons in words.

1. find angle a

a = ______
reason ______

1. find angle a

a = ______
reason ______

1. find angle y

y = ______
reason ______

Answer:

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<reasoning>
The provided image is upside down. Let's orient ourselves and solve each numbered question from 9 to 15.

Calculate composite shape area

Using the Area Decomposition knowledge point.
The shape is decomposed into a central rectangle and two triangles on the sides:

• Central rectangle:

\[
\text{Width} = 4\text{ m},\quad \text{Height} = 6\text{ m}
\]
\[
\text{Area}_{\text{rect}} = 4 \times 6 = 24\text{ m}^2
\]

• Left triangle:

\[
\text{Base} = 2\text{ m},\quad \text{Height} = 6\text{ m}
\]
\[
\text{Area}_{\text{left}} = \frac{1}{2} \times 2 \times 6 = 6\text{ m}^2
\]

• Right triangle:

\[
\text{Base} = 2\text{ m},\quad \text{Height} = 6\text{ m}
\]
\[
\text{Area}_{\text{right}} = \frac{1}{2} \times 2 \times 6 = 6\text{ m}^2
\]

• Total Area:

\[
\text{Total Area} = 24 + 6 + 6 = 36\text{ m}^2
\]

Calculate area of the circle

The circle has a radius \(r = 15\text{ cm}\).

• Formula:

\[
\text{Area} = \pi r^2
\]

• Calculation:

\[
\text{Area} = \pi \times 15^2 = 225\pi \approx 706.8583\text{ cm}^2
\]

• Rounded to 2 decimal places:

\[
\text{Area} \approx 706.86\text{ cm}^2
\]

Calculate circumference of the plate

The circular plate has a diameter \(d = 28\text{ cm}\).

• Formula:

\[
\text{Circumference} = \pi d
\]

• Calculation:

\[
\text{Circumference} = \pi \times 28 \approx 87.9646\text{ cm}
\]

• Rounded to 2 decimal places:

\[
\text{Circumference} \approx 87.96\text{ cm}
\]

Calculate volume of the cuboid

The cuboid has dimensions: length = \(9\text{ cm}\), width = \(4\text{ cm}\), height = \(6\text{ cm}\).

• Formula:

\[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
\]

• Calculation:

\[
\text{Volume} = 9 \times 4 \times 6 = 216\text{ cm}^3
\]

Find angle a (Question 13)

The diagram shows a straight line intersected by another line, forming a linear pair.

• Rule:

Angles on a straight line add up to \(180^\circ\).

• Calculation:

\[
a = 180^\circ - 33^\circ = 147^\circ
\]

Find angle a (Question 14)

The diagram shows angles around a point.

• Rule:

Angles around a point add up to \(360^\circ\).

• Calculation:

\[
a = 360^\circ - 99^\circ = 261^\circ
\]

Find angle y (Question 15)

The diagram shows a triangle with interior angles \(20^\circ\), \(50^\circ\), and \(y\).

• Rule:

The sum of interior angles in a triangle is \(180^\circ\).

• Calculation:

\[
y = 180^\circ - (20^\circ + 50^\circ) = 110^\circ
\]
</reasoning>

<answer>

Question 9

\(36\text{ m}^2\)

Question 10

\(706.86\text{ cm}^2\)

Question 11

\(87.96\text{ cm}\)

Question 12

\(216\text{ cm}^3\)

Question 13

\(a = 147^\circ\)
Reason: Angles on a straight line add up to \(180^\circ\).

Question 14

\(a = 261^\circ\)
Reason: Angles around a point add up to \(360^\circ\).

Question 15

\(y = 110^\circ\)
Reason: Angles in a triangle add up to \(180^\circ\).
</answer>

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