Post on 06-Feb-2016
description
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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