Use this formula to check your answers in the Figure it Out on page 39.

Question

Homi · Accepted Answer

We will use the formula for the area of a square to check the answers from the "Figure it Out" section.

Step 1 — State the formula for the area of a square

The area of a square is calculated by multiplying its side length by itself. Let $s$ represent the side length of a square.

$\text{Area of a square} = s \times s$

$= s^2$

$\boxed{\text{Area} = s^2}$

Diagram 1

Step 2 — Identify the shapes and their dimensions

The diagram shows two squares. Each square is divided into two right-angled triangles by a diagonal cut. Let us assume the "Figure it Out" section provides the side length for each square. Let the side length of the square containing triangles 1 and 2 be $s_1$ . Let the side length of the square containing triangles 3 and 4 be $s_2$ .

Diagram 2

Step 3 — Apply the formula to check the answers

To check the answer for the area of the first square, we substitute its side length $s_1$ into the formula. Suppose the "Figure it Out" section gives an answer $A_1$ for the area of the first square.

$\text{Calculated Area}_1 = s_1^2$

We compare this calculated value with the given answer $A_1$ . If $\text{Calculated Area}_1 = A_1$ , then the answer is correct.

Similarly, for the second square, we use its side length $s_2$ . Suppose the "Figure it Out" section gives an answer $A_2$ for the area of the second square.

$\text{Calculated Area}_2 = s_2^2$

We compare this calculated value with the given answer $A_2$ . If $\text{Calculated Area}_2 = A_2$ , then the answer is correct.

If the "Figure it Out" section also asks for the area of individual triangles (like triangle 1), we can use the fact that each triangle is half the area of its square. So, $\text{Area of triangle 1} = \frac{1}{2} s_1^2$ . We would then compare this with the given answer for triangle 1.

Answer

(i) To check the answer for the area of the first square, use the formula $s_1^2$ and compare it with the given value. (ii) To check the answer for the area of the second square, use the formula $s_2^2$ and compare it with the given value. (iii) To check the answer for the area of triangle 1, calculate $\frac{1}{2} s_1^2$ and compare it with the given value.

Question 14

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