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Math  /  Geometry

QuestionFind the perimeter and area of the figure pictured below.
Perimeter == □\square m
Area == □\square m2\mathrm{m}^{2}

Studdy Solution

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 m−5 m=4 m 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 m−2 m=10 m 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:
Perimeter=9 m+12 m+5 m+2 m+4 m+10 m \text{Perimeter} = 9 \, \text{m} + 12 \, \text{m} + 5 \, \text{m} + 2 \, \text{m} + 4 \, \text{m} + 10 \, \text{m}
=42 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 m×2 m 9 \, \text{m} \times 2 \, \text{m} - Rectangle 2: 5 m×10 m 5 \, \text{m} \times 10 \, \text{m}

STEP 6

Calculate the area of each simpler shape and sum them up:
- Area of Rectangle 1:
Area1=9 m×2 m=18 m2 \text{Area}_1 = 9 \, \text{m} \times 2 \, \text{m} = 18 \, \text{m}^2
- Area of Rectangle 2:
Area2=5 m×10 m=50 m2 \text{Area}_2 = 5 \, \text{m} \times 10 \, \text{m} = 50 \, \text{m}^2
- Total Area:
Total Area=Area1+Area2=18 m2+50 m2=68 m2 \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:
42 m \boxed{42 \, \text{m}}
The area of the figure is:
68 m2 \boxed{68 \, \text{m}^2}

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