Measurements

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Questions and Answers

What is the area of a rectangle that measures 10 cm by 2 cm?

10 cm²
22 cm²
20 cm² (correct)
12 cm²

If a square has an area of 25 cm², what is the length of one side?

5 cm (correct)
12.5 cm
6 cm
10 cm

Which of the following correctly describes how to calculate the area of shapes on a centimetre grid?

Use the formula $Area = base + height$
Add all the lengths together
Count the number of squares that fit inside the shape (correct)
Multiply the perimeter by the height

If a rectangle has a length of 3.5 cm and a width of 2 mm, what must be done before calculating its area?

Convert all measurements to the same unit (A) Signup and view all the answers

What is the total area of a rectangle measuring 12 cm in length and 3 cm in width?

36 cm² (C) Signup and view all the answers

Which of the following expressions correctly represents the area of a shape if the dimensions are given in centimeters?

$Area = length \times width$ (D) Signup and view all the answers

What is the height of the rectangular part of the window?

2 m (C) Signup and view all the answers

What is the total perimeter of the window, rounded to the nearest 1 cm?

6.28 m (C) Signup and view all the answers

What is the angle measure of sector B?

140° (A) Signup and view all the answers

For a circle with a radius of 3 m, what is the arc length for an angle of 140°?

3.06 m (C) Signup and view all the answers

Find the length of the arc for a 100° angle with a radius of 7 mm, correct to two decimal places.

1.74 mm (D) Signup and view all the answers

Determine the arc length for an angle of 80° with a radius of 4 m, correct to two decimal places.

2.80 m (C) Signup and view all the answers

What is the length of the arc for a sector with a central angle of 85° and a radius of 1.3 m?

0.93 m (B) Signup and view all the answers

If the perimeter of a rectangular shape is calculated, which formula is used?

2(Length + Width) (A) Signup and view all the answers

Which of the following is NOT a measurement given in the content?

5 m (C) Signup and view all the answers

What is the formula to find the circumference of the composite shape mentioned?

P = 2πr + 4r (A) Signup and view all the answers

Why is the perimeter of the shape expressed as P = 2πr?

It accounts only for the circular parts of the shape. (D) Signup and view all the answers

Given the arc length of 4m and the angle of 30°, what is the radius?

4m (D) Signup and view all the answers

What is the total perimeter described in the workings shown for the composite shape?

20 + 8π cm (C) Signup and view all the answers

When calculating the radius of the sector with a 100° angle and an unspecified length, what is necessary?

The arc length measurement is essential. (B) Signup and view all the answers

If a sector has an angle of 60° and a radius of r, which formula describes the arc length?

Arc length = (2πr)(60/360) (A) Signup and view all the answers

In the provided composite shape, which measurement represents a straight edge?

4 cm (D) Signup and view all the answers

For a shape composed of two circular sectors, what contributes primarily to the perimeter?

Both the circular and straight segments. (C) Signup and view all the answers

What is the area of grass to be laid in a rectangular soccer field that is 100 m long and 50 m wide?

5000 m² (A) Signup and view all the answers

If 200 square tiles measure 10 cm by 10 cm each, what is the total area of the flooring that is tiled?

200 m² (D) Signup and view all the answers

How many square meters are there in 20,000 m²?

2 hectares (C) Signup and view all the answers

What is the area of a square window with a side length of 50 cm?

2500 cm² (B) Signup and view all the answers

If a square has a perimeter of 20 cm, what is its area?

25 cm² (D) Signup and view all the answers

How many litres of paint will Troy need to purchase if he is painting a wall that is 11 m long and 3 m high, requiring two coats and coverage of 15 m² per litre?

4 litres (D) Signup and view all the answers

What is the cost of carpeting a rectangular room that is 6 m long and 5 m wide if the carpet costs $70 per square metre?

$840 (D) Signup and view all the answers

What is the area in hectares of a rectangular piece of land measuring 200 m by 400 m?

8 hectares (D) Signup and view all the answers

Study Notes

Arc Length Calculations

The arc length of a circle is a portion of the circle's circumference.
To calculate the arc length, use the formula: Arc Length = (θ/360°) * 2πr where θ is the central angle in degrees and r is the radius of the circle.
The text provides several examples of calculating arc lengths for different central angles and radii.

Perimeter of Sectors and Composite Shapes

A sector of a circle is a region bounded by two radii and an arc.
To calculate the perimeter of a sector, add the lengths of the two radii and the arc length.
The text provides examples of calculating the perimeter of sectors and composite shapes involving different combinations of arcs, circles, and rectangles.

Area of Squares and Rectangles

The area of a square is calculated by multiplying the side length by itself: Area = side * side
The area of a rectangle is calculated by multiplying the length by the width: Area = length * width
The text includes examples of finding the area of squares and rectangles with different side lengths and dimensions.

Area Conversions

There are 10,000 square meters (m²) in one hectare (ha).
This information is used to convert area measurements from square meters to hectares.

Problems involving area are presented to illustrate how the concepts can be applied in real-world scenarios.
These problems include finding the area of a soccer field, a window, and a tiled floor.
Other problems focus on relationships between the perimeter and area of a square, and on calculating the cost of carpeting or painting based on the area to be covered.

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