Questions: Find the perimeter and area of the figure pictured below. Perimeter = square m Area = square m^2

Solution Steps

The figure is an L-shaped polygon. The dimensions given are:

• Vertical segment: 10 m
• Horizontal segment: 12 m
• Small vertical segment: 2 m
• Small horizontal segment: 3 m

To find the perimeter, add the lengths of all the outer sides:

• Vertical sides: 10 m + 2 m = 12 m
• Horizontal sides: 12 m + 3 m = 15 m
• The remaining sides are the same as the given dimensions.

So, the perimeter is: \[ 10 \, \text{m} + 2 \, \text{m} + 3 \, \text{m} + 12 \, \text{m} + 10 \, \text{m} + 12 \, \text{m} = 39 \, \text{m} \]

To find the area, divide the L-shaped figure into two rectangles:

• Rectangle 1: 10 m by 12 m
• Rectangle 2: 2 m by 3 m

Calculate the area of each rectangle:

• Area of Rectangle 1: \( 10 \, \text{m} \times 12 \, \text{m} = 120 \, \text{m}^2 \)
• Area of Rectangle 2: \( 2 \, \text{m} \times 3 \, \text{m} = 6 \, \text{m}^2 \)

Add the areas of the two rectangles: \[ 120 \, \text{m}^2 + 6 \, \text{m}^2 = 126 \, \text{m}^2 \]

Final Answer