Question

question 7

find the perimeter and area of the figure pictured below.

perimeter = m
area = m^2

Explanation:

Find the missing side lengths

The figure is an L-shaped polygon. We need to determine the lengths of the two inner sides that are not explicitly labeled.

• The total height on the left is \(11.3\text{ m}\). The height of the right vertical segment is \(2.7\text{ m}\). Thus, the inner vertical side length is:

$$11.3\text{ m} - 2.7\text{ m} = 8.6\text{ m}$$

• The total width at the bottom is \(9.1\text{ m}\). The width of the top horizontal segment is \(2.4\text{ m}\). Thus, the inner horizontal side length is:

$$9.1\text{ m} - 2.4\text{ m} = 6.7\text{ m}$$

Calculate the perimeter

The perimeter is the sum of all outer boundary segments of the shape. Summing the six sides:

• Left vertical: \(11.3\text{ m}\)
• Top horizontal: \(2.4\text{ m}\)
• Inner vertical: \(8.6\text{ m}\)
• Inner horizontal: \(6.7\text{ m}\)
• Right vertical: \(2.7\text{ m}\)
• Bottom horizontal: \(9.1\text{ m}\)

$$\text{Perimeter} = 11.3 + 2.4 + 8.6 + 6.7 + 2.7 + 9.1 = 40.8\text{ m}$$

Calculate the area

We can split the L-shape vertically into two simpler rectangles:

1. Left vertical rectangle:

• Width = \(2.4\text{ m}\)
• Height = \(11.3\text{ m}\)
• \(\text{Area}_1 = 2.4\text{ m} \times 11.3\text{ m} = 27.12\text{ m}^2\)

1. Right horizontal rectangle:

• Width = \(9.1\text{ m} - 2.4\text{ m} = 6.7\text{ m}\)
• Height = \(2.7\text{ m}\)
• \(\text{Area}_2 = 6.7\text{ m} \times 2.7\text{ m} = 18.09\text{ m}^2\)

Summing the two areas:

$$\text{Total Area} = 27.12 + 18.09 = 45.21\text{ m}^2$$

Answer:

Perimeter = 40.8 m
Area = 45.21 \(\text{m}^2\)