Question
What is the total area of four white triangles if 𝑥 = 12 𝑐𝑚?
Hint:
The methods used to find the product of binomials are called special products.
Multiplying a number by itself is often called squaring.
For example (x + 3)(x + 3) = (x + 3)2
Area of a square = (side)2
The correct answer is: 180 cm2.
The area of the outer square of side x+6 cm = (x+6)2
(x+6)2 = (x+6)(x+6) = x(x+6) +6(x+6)
= x(x) + x(6) +6(x) +6(6)
= x2 + 6x + 6x + 36
= x2 + 12x + 36
The area of the inner square of side x cm = x2
Now, Total area of four white triangles = Area of the outer square - area of the inner square
= x2 + 12x + 36 - x2
= 12x + 36
Given that x =12 cm
So, Total area of four white triangles = 12(12) + 36
= 144 + 36 = 180 cm2
Final Answer:
Hence, the total area of four white triangles is 180 cm2.
The area of the inner square of side x cm = x2
Now, Total area of four white triangles = Area of the outer square - area of the inner square
Given that x =12 cm
So, Total area of four white triangles = 12(12) + 36
Final Answer:
Hence, the total area of four white triangles is 180 cm2.
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