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)

= x^{2} + 6x + 6x + 36

= x^{2} + 12x + 36

The area of the inner square of side x cm = x^{2}

Now, Total area of four white triangles = Area of the outer square - area of the inner square

= x^{2} + 12x + 36 - x^{2}

= 12x + 36

Given that x =12 cm

So, Total area of four white triangles = 12(12) + 36

= 144 + 36 = 180 cm^{2}

Final Answer:

Hence, the total area of four white triangles is 180 cm^{2}.

^{2}+ 6x + 6x + 36

^{2}+ 12x + 36

The area of the inner square of side x cm = x

^{2}

Now, Total area of four white triangles = Area of the outer square - area of the inner square

^{2}+ 12x + 36 - x

^{2}

Given that x =12 cm

So, Total area of four white triangles = 12(12) + 36

^{2}

Final Answer:

Hence, the total area of four white triangles is 180 cm

^{2}.

### Related Questions to study

### Describe the possible values of x.

### Describe the possible values of x.

### What expression represents the total area of the four white triangles?

### What expression represents the total area of the four white triangles?

### Write the product in the standard form. (𝑥^{2} − 2𝑦)(𝑥^{2} + 2𝑦)

This question can be easily solved by using the formula

(a + b)(a - b) = a2 - b2

### Write the product in the standard form. (𝑥^{2} − 2𝑦)(𝑥^{2} + 2𝑦)

This question can be easily solved by using the formula

(a + b)(a - b) = a2 - b2

### Write the product in the standard form. (𝑥 − 2.5)(𝑥 + 2.5)

This question can be easily solved by using the formula

(a + b)(a - b) = a2 - b2

### Write the product in the standard form. (𝑥 − 2.5)(𝑥 + 2.5)

This question can be easily solved by using the formula

(a + b)(a - b) = a2 - b2

### Describe the possible lengths of the third side of the triangle given the lengths of the other two sides.

5 inches, 12 inches

### Describe the possible lengths of the third side of the triangle given the lengths of the other two sides.

5 inches, 12 inches

### Write the product in the standard form. (3𝑎 − 4𝑏)(3𝑎 + 4𝑏)

This question can be easily solved by using the formula

(a + b)(a - b) = a2 - b2

### Write the product in the standard form. (3𝑎 − 4𝑏)(3𝑎 + 4𝑏)

This question can be easily solved by using the formula

(a + b)(a - b) = a2 - b2

### Write the product in the standard form.

This question can be easily solved by using the formula

(a + b)(a - b) = a2 - b2

### Write the product in the standard form.

This question can be easily solved by using the formula

(a + b)(a - b) = a2 - b2

### How is it possible that the sum of two quadratic trinomials is a linear binomial?

### How is it possible that the sum of two quadratic trinomials is a linear binomial?

### If (3x-4) (5x+7) = 15x^{2}-ax-28, so find the value of a?

### If (3x-4) (5x+7) = 15x^{2}-ax-28, so find the value of a?

### The difference of x^{4}+2x^{2}-3x+7 and another polynomial is x^{3}+x^{2}+x-1. What is the

another polynomial?

### The difference of x^{4}+2x^{2}-3x+7 and another polynomial is x^{3}+x^{2}+x-1. What is the

another polynomial?

### Use the product of sum and difference to find 83 × 97.

This question can be easily solved by using the formula

(a + b)(a - b) = a2 - b2

### Use the product of sum and difference to find 83 × 97.

This question can be easily solved by using the formula

(a + b)(a - b) = a2 - b2

### Determine the gradient and y-intercept from the following equation: 4x + y = -10

### Determine the gradient and y-intercept from the following equation: 4x + y = -10

### Use the product of sum and difference to find 32 × 28.

This question can be easily solved by using the formula

(a + b)(a - b) = a2 - b2

### Use the product of sum and difference to find 32 × 28.

This question can be easily solved by using the formula

(a + b)(a - b) = a2 - b2