Matemática Elementar

Problema 1

Count the unit squares to find the area of the rectangle.

\hline \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} \\ \hline \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} \\ \hline \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} \\ \hline \end{array}$$ Number of rows: $\underline{\quad}$ Number of columns: $\underline{\quad}$ Area $= \underline{\quad} \times \underline{\quad} = \underline{\quad}$ square units

Problemas

1. Count the unit squares to find the area of the rectangle.

\hline \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} \\ \hline \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} \\ \hline \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} & \phantom{X} \\ \hline \end{array}$$ Number of rows: $\underline{\quad}$ Number of columns: $\underline{\quad}$ Area $= \underline{\quad} \times \underline{\quad} = \underline{\quad}$ square units

2. Use the formula $A = l \times w$ to find the area.

a) A rectangle with length $8$ cm and width $5$ cm.

$A = \underline{\quad} \times \underline{\quad} = \underline{\quad} \text{ cm}^2$

b) A square with side length $6$ inches.

$A = \underline{\quad} \times \underline{\quad} = \underline{\quad} \text{ in}^2$

3. A garden has the shape shown. Find its perimeter.

\underbrace{\hspace{4cm}}_{9 \text{ ft}} \\ \left| \phantom{\frac{X}{X}} \right. \hspace{3cm} \left. \phantom{\frac{X}{X}} \right| \; 4 \text{ ft on each side} \\ \underbrace{\hspace{4cm}}_{9 \text{ ft}} \end{array}$$ The rectangle is $9$ ft long and $4$ ft wide. $$P = \underline{\quad} + \underline{\quad} + \underline{\quad} + \underline{\quad} = \underline{\quad} \text{ ft}$$ Or use: $P = 2 \times (l + w) = 2 \times (\underline{\quad} + \underline{\quad}) = \underline{\quad}$ ft

4. A classroom floor is $12$ meters long and $8$ meters wide.

a) What is the area of the floor?

$A = \underline{\quad} \times \underline{\quad} = \underline{\quad} \text{ m}^2$

b) What is the perimeter of the floor?

$P = 2 \times (\underline{\quad} + \underline{\quad}) = \underline{\quad} \text{ m}$

c) If carpet costs $\$ 3$ per square meter, how much will it cost to carpet the whole floor?

$\text{Cost} = \underline{\quad} \times \$3 = \$\underline{\quad}$

5. Two rectangles have the same area of $24$ square units, but different shapes.

Rectangle A: length $= 8$ , width $= \underline{\quad}$

Rectangle B: length $= 6$ , width $= \underline{\quad}$

Find the perimeter of each:

$P_A = 2 \times (8 + \underline{\quad}) = \underline{\quad} \text{ units}$

$P_B = 2 \times (6 + \underline{\quad}) = \underline{\quad} \text{ units}$

Are the perimeters the same? Circle: Yes / No

6. A shape is made of two rectangles joined together.

What is the total area of the whole shape?

$A_1 = \underline{\quad} \times \underline{\quad} = \underline{\quad} \text{ cm}^2$

$A_2 = \underline{\quad} \times \underline{\quad} = \underline{\quad} \text{ cm}^2$

$A_{\text{total}} = \underline{\quad} + \underline{\quad} = \underline{\quad} \text{ cm}^2$

Gabarito — Area and Perimeter

1. The rectangle has $3$ rows and $5$ columns.

$A = 3 \times 5 = \mathbf{15} \text{ square units}$

2. a) $A = 8 \times 5 = \mathbf{40} \text{ cm}^2$

b) $A = 6 \times 6 = \mathbf{36} \text{ in}^2$

(A square has equal length and width, so both dimensions are $6$ .)

3. Add all four sides: $9 + 4 + 9 + 4 = 26$ ft.

$P = 9 + 4 + 9 + 4 = \mathbf{26} \text{ ft}$

Using the formula: $P = 2 \times (9 + 4) = 2 \times 13 = \mathbf{26}$ ft ✓

4. a) $A = 12 \times 8 = \mathbf{96} \text{ m}^2$

b) $P = 2 \times (12 + 8) = 2 \times 20 = \mathbf{40}$ m

c) Cost $= 96 \times \$ 3 = \mathbf{$288}$

5. Both rectangles have area $= 24$ square units.

Perimeters: $P_A = 2 \times (8 + 3) = 2 \times 11 = \mathbf{22} \text{ units}$ $P_B = 2 \times (6 + 4) = 2 \times 10 = \mathbf{20} \text{ units}$

The perimeters are not the same. Same area does not mean same perimeter.

6. $A_1 = 5 \times 3 = 15 \text{ cm}^2$ $A_2 = 4 \times 2 = 8 \text{ cm}^2$ $A_{\text{total}} = 15 + 8 = \mathbf{23} \text{ cm}^2$