Shape and Space

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1 of 84 Shape and Space Triangles

description

Shape and Space. Triangles. terms. Tri angle - A 3-sided polygon (a flat shape with straight sides) Square ( spanish ) - A 4-sided flat shape with straight sides where: all sides have equal length, and every angle is a right angle (90°) - PowerPoint PPT Presentation

Transcript of Shape and Space

Page 1: Shape and Space

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Shape and Space

Triangles

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terms Triangle - A 3-sided polygon (a flat shape with

straight sides) Square (spanish) - A 4-sided flat shape with

straight sides where: all sides have equal length, and every angle is a right angle (90°)

Perpendicular ┴ - at an angle of 90° to a given line, plane, or surface

Base - The surface that a solid object stands on, or the bottom line of a shape such as a triangle or rectangle.

Height - The vertical distance from top to bottom

Right angle - An angle which is equal to 90°, one quarter of a full revolution.

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The perimeter of a triangle is the measure around the triangle

= a + b + c

a b

c

PERIMETERexample 1A = 2B = 5C = 5Perimeter = ?

12

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The perimeter of a triangle is the measure around the triangle

= a + b + c

a b

c

PERIMETER

Check 1A = 5B = 5C = 5Perimeter = ?

Check 2A = 5B = 10C = 10Perimeter = ?

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To find the area of a triangle:

The (h) height = the perpendicular distance from the opposite vertex to the (b) base

h

b

AREA

exampleB = 10H = 7½ x 10 x 7 = ?.5 x 10 x 7 = ?

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Area of a right-angled triangle

What proportion of this rectangle has been shaded?

8 cm

4 cm

What is the shape of the shaded part?

What is the area of this right-angled triangle?

Area of the triangle = × 8 × 4 = 12 4 × 4 = 16 cm2

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We can use a formula to find the area of a right-angled triangle:

Area of a right-angled triangle

base, b

height, h

Area of a triangle = 12

× base × height

= 12 bh

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Area of a right-angled triangle

Calculate the area of this right-angled triangle.

6 cm

8 cm

10 cm

To work out the area of this triangle we only need the length of the base and the height.

We can ignore the third length opposite the right angle.

Area = 12 × base × height

= × 8 × 612 = 24 cm2

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Area of a triangle

What proportion of this rectangle has been shaded?

8 cm

4 cm

Drawing a line here might help.

What is the area of this triangle?

Area of the triangle = × 8 × 4 = 12 4 × 4 = 16 cm2

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Area of a triangle

The area of any triangle can be found using the formula:

Area of a triangle = × base × perpendicular height12

base

perpendicular height

Or using letter symbols,

Area of a triangle = bh12

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Any side of the triangle can be taken as the base, as long as the height is perpendicular to it:

The area of a triangle

b

h

bh b

h

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Area of a triangle

What is the area of this triangle?

Area of a triangle = bh12

7 cm

6 cm

= 12 × 7 × 6

= 21 cm2

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Area of a triangle

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The area of a triangle

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area = ½ ( 3 )( 6 ) = 9 square units

area = ½ ( 5 )( 9 ) = 22 ½ square units

area = ½ ( h )( b )

area = ½ ( 4 )( 7 ) = 14 square units