Math Snap

STEP 1

1. The figure is an L-shaped polygon.
2. The given dimensions are accurate and correspond to the sides of the L-shape.

STEP 2

1. Determine the missing side lengths.
2. Calculate the perimeter of the L-shaped figure.
3. Divide the L-shaped figure into simpler shapes to calculate the area.
4. Calculate the area of each simpler shape and sum them up.

STEP 3

Determine the missing side lengths:
- The L-shape consists of two rectangles. The longer vertical side is 9 m, and the shorter vertical side is 5 m. Therefore, the missing vertical side is:
$$9 \, \text{m} - 5 \, \text{m} = 4 \, \text{m}$$ - The longer horizontal side is 12 m, and the shorter horizontal side is 2 m. Therefore, the missing horizontal side is:
$$12 \, \text{m} - 2 \, \text{m} = 10 \, \text{m}$$

STEP 4

Calculate the perimeter of the L-shaped figure:
- The perimeter is the sum of all outer side lengths:
$$\text{Perimeter} = 9 \, \text{m} + 12 \, \text{m} + 5 \, \text{m} + 2 \, \text{m} + 4 \, \text{m} + 10 \, \text{m}$$ $$= 42 \, \text{m}$$

STEP 5

Divide the L-shaped figure into simpler shapes to calculate the area:
- Divide the L-shape into two rectangles:
- Rectangle 1: $9 \, \text{m} \times 2 \, \text{m}$
- Rectangle 2: $5 \, \text{m} \times 10 \, \text{m}$

Calculate the area of each simpler shape and sum them up:
- Area of Rectangle 1:
$$\text{Area}_1 = 9 \, \text{m} \times 2 \, \text{m} = 18 \, \text{m}^2$$ - Area of Rectangle 2:
$$\text{Area}_2 = 5 \, \text{m} \times 10 \, \text{m} = 50 \, \text{m}^2$$ - Total Area:
$$\text{Total Area} = \text{Area}_1 + \text{Area}_2 = 18 \, \text{m}^2 + 50 \, \text{m}^2 = 68 \, \text{m}^2$$ The perimeter of the figure is:
$$\boxed{42 \, \text{m}}$$ The area of the figure is:
$$\boxed{68 \, \text{m}^2}$$