Area and perimeter
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This document discusses calculating the areas and perimeters of various shapes. It provides examples of finding the perimeter by counting sides and finding the area by counting squares for both regular and irregular shapes. It also introduces calculating the area of rectangles using the formula of length x width and calculating the total area of composite shapes by finding the individual areas and summing them.
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The document discusses perimeter and area, defining perimeter as the distance all the way around a figure and area as the number of square units needed to cover a surface. It provides formulas for calculating the perimeter and area of squares and rectangles. The perimeter of a square is calculated as P = 4s and the area as A = s^2. For a rectangle, the perimeter formula is P = 2w + 2l and the area formula is A = lw.
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This powerpoint document discusses measuring shapes and space by explaining perimeter, area, and volume. It provides formulas and examples for calculating the perimeter and area of various shapes including rectangles, triangles, trapezoids, circles, and composite shapes made up of multiple basic shapes. Key formulas presented include the circumference of a circle being equal to 2πr or the diameter, and the area of a circle being equal to πr2. An example composite shape is used to demonstrate calculating total area by finding the individual areas of each component shape.
PERIMETER OF PLANE SHAPES
This document defines perimeter and explains how to calculate the perimeter of common shapes such as rectangles, triangles, circles, and composite shapes. It provides examples of calculating perimeters of various shapes, including word problems involving finding the total length of paths, boxes, photographs, and picture frames given measurements of the sides or diameters. The key points are that perimeter is the distance around an object and is calculated by adding all the lengths of the sides for simple shapes or the outer lengths for composite shapes.
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This document discusses calculating the surface area and volume of cuboids and other 3D shapes. It provides examples of finding the surface area of cuboids by adding the areas of each face. The formula for surface area of a cuboid is given as 2lw + 2hw + 2lh, where l, w, and h are the length, width, and height. Examples are also given for finding the volume of cuboids using the formula length × width × height and relating volume to water displacement.
Area
The document discusses how to calculate the area of 2D shapes by breaking them down into rectangles. It explains that area is measured in square units and is calculated by multiplying the length and width of a rectangle. Examples are provided of calculating the area of rectangles and more complex shapes by breaking them into individual rectangles and adding the areas.
Pythagoras' Theorem
Pythagoras' theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The document explains how to use Pythagoras' theorem to find the length of any side of a right-angled triangle if the other two sides are known. It provides examples of calculating missing side lengths and notes that the theorem can be rearranged to find a non-hypotenuse side if the hypotenuse is known instead. Correct notation for showing working is emphasized.
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Area and perimeter
- 2. 8 cm 6 cm 8 cm 6 cm The perimeter of the shape is 8 + 6 + 8 + 6 = 28cm. First we need to find he length of each side by counting the squares. The distance around the outside of a shape is called the perimeter.
- 3. What is the perimeter of each of these shapes? Your teacher will give you copy of the worksheet. 18cm 18cm 18cm 22cm 26cm
- 4. Now find the perimeter of these shapes. They are not drawn to scale. Perimeter = 18cm Perimeter = 22cm Perimeter = 28cm 3cm 3cm 3cm 3cm 3cm 3cm 5cm 7cm 7cm 3cm 4cm 4cm 4cm 4cm 3cm 3cm 3cm 3cm
- 5. The area of the shape is 18cm 2 . To find out how much shape is inside we can count the squares. The area of a shape is the amount of space inside it.
- 6. What is the area of each of these shapes? Your teacher will give you copy of the worksheet. 12cm 2 26cm 2 26cm 2
- 7. To find the area of an irregular shape you first count the full squares inside it. This is an irregular shape. This means that the sides aren’t straight.
- 8. The area of the shape is 60cm 2 . You then count all the other squares which have more than half the area covered.
- 9. What is the area of each of these shapes? Your teacher will give you copy of the worksheet. 24cm 2 25cm 2 22cm 2 35cm 2
- 10. The area of the shape is 48cm 2 . The rectangle is made of 6 rows of 8 squares. To work out the number of squares we times 6 by 8. Counting each square can take a long time. Does anyone know a quicker way?
- 11. What is the area of each of these shapes? Your teacher will give you copy of the worksheet. 20cm 2 18cm 2 14cm 2 30cm 2 22cm 2
- 12. We can work out the area of a rectangle without the grid. length width Area = length x width
- 13. Now work out the area of these rectangles. They are not drawn to scale . 36cm 2 35cm 2 20cm 2 25cm 2 4cm 9cm 7cm 5cm 5cm 4cm 2cm 12.5cm
- 14. A shape that is made from other shapes is known as a composite shape. To find the area of this shape we have to split it up into two rectangles. 10cm 8cm 8cm 2cm 4cm 4cm Area = 4 x 10 40cm 2 Area = 4 x 8 32cm 2 Total area = 40 + 32 = 72 cm 2
- 15. Find the area and perimeter of each of these shapes? Your teacher will give you copy of the worksheet. 9cm 5cm 5cm 2cm 4cm 5cm 4cm 2cm 11cm 7cm 4cm 3cm 3cm 3cm 7cm 4cm 6cm 6cm 11cm 2cm 4cm 5cm
- 16. 9cm 5cm 5cm 2cm 4cm 5cm 4cm 2cm Area = 5 x 9 45cm 2 Area = 4 x 5 20cm 2 Total area = 45 + 20 = 65 cm 2 Perimeter = 36 cm
- 17. Area = 2 x 5 10cm 2 Area = 6 x 6 36cm 2 Total area = 10 + 36 = 46 cm 2 Perimeter = 34 cm 6cm 6cm 11cm 2cm 4cm 5cm
- 18. 11cm 7cm 4cm 3cm 3cm 3cm 7cm Total area = 28 + 16 + 21 = 65 cm 2 Perimeter = 42 cm Area = 4 x 7 Area = 4 x 4 4cm Area = 3 x 7 21cm 2 28cm 2 16cm 2 There is another way of doing this question.
- 19. 11cm 7cm 4cm 3cm 3cm 3cm 7cm Total area = 77 – 12 = 65 cm 2 Perimeter = 42 cm Area = 7 x 11 Area = 3 x 4 4cm 77cm 2 12cm 2
- 20. Well Done
- 21. w o r k s h e e t o n e
- 22. w o r k s h e e t t w o
- 23. w o r k s h e e t t h r e e
- 24. 9cm 5cm 5cm 2cm 4cm 5cm 4cm 2cm 11cm 7cm 4cm 3cm 3cm 4cm 3cm 7cm w o r k s h e e t f o u r 6cm 6cm 11cm 2cm 4cm 5cm
- 25. Review What is the area of the moon? _____________________cm 2 What is the area of the rectangle? _____________________cm 2 What is the perimeter of the rectangle? _____________________cm Name:____________________
- 26. 4cm 4cm 4cm 6cm 8cm 2cm What is the area of the compound shape? _____________________cm 2 What is the perimeter of the compound shape? _____________________cm What is the area of the house? _____________________cm 2