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primary 6 | Maths
| Measurement
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Date Posted: 3 years ago
Views: 264
½ × 11 cm × 11 cm = ½ × 121 cm²
= 60.5 cm²
= 60.5 cm²
Reason : The combined area of the shaded triangles is equal to half the area of the square.
Both shaded triangles have same base length of 11 cm.
Their combined height (which is 90°/perpendicular to the base) is equal to the length of the square.
½ × 11 cm × (height of smaller ▲) + ½ × 11 cm × (height of bigger shaded ▲)
= ½ × 11 cm × (height of bigger of smaller ▲ + bigger ▲)
= ½ × 11 cm × 11cm
= ½ × area of the square.
The same reasoning is used for the two unshaded △s.
This is called the distributive law of multiplication.
Both shaded triangles have same base length of 11 cm.
Their combined height (which is 90°/perpendicular to the base) is equal to the length of the square.
½ × 11 cm × (height of smaller ▲) + ½ × 11 cm × (height of bigger shaded ▲)
= ½ × 11 cm × (height of bigger of smaller ▲ + bigger ▲)
= ½ × 11 cm × 11cm
= ½ × area of the square.
The same reasoning is used for the two unshaded △s.
This is called the distributive law of multiplication.
Example : lets say the height of the smaller ▲ is 4 cm.
Then height of bigger ▲ is 11 cm - 4 cm = 7 cm
Combined area
= ½ × 11 cm × 7 cm + ½ × 11 cm × 4 cm
= ½ × 77 cm² + ½ × 44 cm²
= 38.5 cm² + 22 cm²
= 60.5 cm²
But notice that this is the same as :
½ × 11 cm × (7 cm + 4 cm)
= ½ × 11 cm × 11 cm
= ½ × 121 cm²
= 60.5 cm²
We can rewrite ½ × 11cm as 6½ cm and then it just becomes a case of adding 7 groups of 6½ to 4 groups of 6½, to get 11 groups of 6½
No matter what height each ▲ has, the total is always 11 cm.
Then height of bigger ▲ is 11 cm - 4 cm = 7 cm
Combined area
= ½ × 11 cm × 7 cm + ½ × 11 cm × 4 cm
= ½ × 77 cm² + ½ × 44 cm²
= 38.5 cm² + 22 cm²
= 60.5 cm²
But notice that this is the same as :
½ × 11 cm × (7 cm + 4 cm)
= ½ × 11 cm × 11 cm
= ½ × 121 cm²
= 60.5 cm²
We can rewrite ½ × 11cm as 6½ cm and then it just becomes a case of adding 7 groups of 6½ to 4 groups of 6½, to get 11 groups of 6½
No matter what height each ▲ has, the total is always 11 cm.
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Alternative approach to the one that I left in the question's comments section:
The whole square can be divided into 4 rectangles. Notice that for every shaded part (▲) , there is an identical unshaded part with the same area (△). So all the shaded ▲s form up half the total area of the square. (The other half is made up of unshaded △s)
So area of shaded = area of unshaded = ½ × 11 cm × 11 cm = 60.5 cm²
The whole square can be divided into 4 rectangles. Notice that for every shaded part (▲) , there is an identical unshaded part with the same area (△). So all the shaded ▲s form up half the total area of the square. (The other half is made up of unshaded △s)
So area of shaded = area of unshaded = ½ × 11 cm × 11 cm = 60.5 cm²
Date Posted:
3 years ago
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