Question

consider the following figure (a rectangle with height 8 m and base 5 m, right angles at corners). (a) find the perimeter (in m) of the figure. \boxed{} m (b) find the area (in m²) of the figure. \boxed{} m²

Explanation:

Part (a): Perimeter of the Rectangle

Step 1: Recall the formula for the perimeter of a rectangle

The formula for the perimeter \( P \) of a rectangle with length \( l \) and width \( w \) is \( P = 2(l + w) \).

Step 2: Identify the length and width

From the figure, the length \( l = 8 \, \text{m} \) and the width \( w = 5 \, \text{m} \).

Step 3: Substitute the values into the formula

Substitute \( l = 8 \) and \( w = 5 \) into \( P = 2(l + w) \):
\[
P = 2(8 + 5)
\]

Step 4: Simplify the expression

First, calculate the sum inside the parentheses: \( 8 + 5 = 13 \). Then multiply by 2: \( 2 \times 13 = 26 \).

Step 1: Recall the formula for the area of a rectangle

The formula for the area \( A \) of a rectangle with length \( l \) and width \( w \) is \( A = l \times w \).

Step 2: Identify the length and width

From the figure, the length \( l = 8 \, \text{m} \) and the width \( w = 5 \, \text{m} \).

Step 3: Substitute the values into the formula

Substitute \( l = 8 \) and \( w = 5 \) into \( A = l \times w \):
\[
A = 8 \times 5
\]

Step 4: Simplify the expression

Calculate the product: \( 8 \times 5 = 40 \).

Answer:

\( 26 \)

Part (b): Area of the Rectangle