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April 9, 2023
Areas
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1. The area of a triangle.
April 9, 2023
A D
B C
4 cm
7 cm
The area of rectangle ABCD is 7 cm × 4 cm
You can make two equal triangles by drawing a diagonal from A to C.The total area of these two triangles will be the same as the area of the original rectangle.The area of one triangle will be…
= 28 cm²
12 7 cm × 4 cm× = 14 cm²
Explanation
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April 9, 2023
This works for all right angle triangles.
5 cm
3 cm
5 cm
4 cm
2.5 cm
4.5 cm
5 cm × 3 cm× = 7.5 cm²
12 5 cm × 4 cm× = 10 cm²
12 2.5 cm × 4.5 cm× = 5.625 cm²
12
Examples
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April 9, 2023
N
OP5 cm 3 cm8 cm
Triangle NOP is not a right angle triangle.You can create two right angle triangles by dividing it in two.Both new triangles have the height of the perpendicular used to divide the original triangle.
The areas of each triangle can be calculated.
5 cm5 cm 5 cm
Explanation
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April 9, 2023
N
OP5 cm 3 cm
The areas of each triangle can be calculated.
5 cm 5 cm
Triangle NOP is not a right angle triangle.You can create two right angle triangles by dividing it in two.Both new triangles have the height of the perpendicular used to divide the original triangle.
Explanation
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April 9, 2023
N
OP5 cm 3 cm
The areas of each triangle can be calculated.
5 cm 5 cm
12 5 cm × 5 cm× = 12.5 cm²
12 3 cm × 5 cm× = 7.5 cm²
The area of triangle NOP =
12.5 cm² + 7.5 cm² = 20 cm²
20 cm²
So
Another way of calculating this area is
12 8 cm × 5 cm× = 20 cm²
8 cm
In fact, you can work out the area of any triangle if you know the perpendicular height, using the formula…
area of the triangle = 12
perpendicular heightbase ××or
A = 12
hb ××
12 × h
b
Explanation
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April 9, 2023
You can use any side of the triangle as the base, from which to work out the perpendicular height.When you calculate the area, make sure that you use the height that corresponds to the base that you choose.
12 ×
hb
h
bh
b
Explanation
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