We read your photo as:

Calculate the perimeter and area of the given L-shaped floor plan.

Mathematics

ScanSolve AI Answer

Answers

3 parts
i

26 m\text{26 m}

ii

34 m2\text{34 m}^2\text{}

iii

GH¢ 680.00\text{GH¢ 680.00}

Step-by-step solution

7 steps

First, let's determine the lengths of the missing sides of the floor plan.
The total top length is 8 m8 \text{ m} and the bottom segment is 5 m5 \text{ m}. So, the inner horizontal segment is 8 m−5 m=3 m8 \text{ m} - 5 \text{ m} = 3 \text{ m}.
The total left vertical length is 5 m5 \text{ m} and the right vertical length is 3 m3 \text{ m}. So, the inner vertical segment is 5 m−3 m=2 m5 \text{ m} - 3 \text{ m} = 2 \text{ m}.

Part i· 2 steps

Perimeter

  1. Identify all side lengths.

    The side lengths are 8 m8 \text{ m}, 3 m3 \text{ m}, 3 m3 \text{ m} (inner horizontal), 2 m2 \text{ m} (inner vertical), 5 m5 \text{ m}, and 5 m5 \text{ m}.

  2. Sum all the side lengths to find the perimeter.

    Perimeter=8 m+3 m+3 m+2 m+5 m+5 m\text{Perimeter} = 8 \text{ m} + 3 \text{ m} + 3 \text{ m} + 2 \text{ m} + 5 \text{ m} + 5 \text{ m} Perimeter=26 m\text{Perimeter} = 26 \text{ m}

    The perimeter of the floor is 26 m\boxed{\text{26 m}}.

Part ii

34 m2\text{34 m}^2\text{}

Area

  1. Divide the L-shaped floor into two rectangles.

    We can divide it into a top rectangle and a bottom-left rectangle.
    Rectangle 1 (top): length 8 m8 \text{ m}, width 3 m3 \text{ m}.
    Rectangle 2 (bottom-left): length 5 m5 \text{ m}, width 5 m−3 m=2 m5 \text{ m} - 3 \text{ m} = 2 \text{ m}.

  2. Calculate the area of each rectangle.

    Area1=8 m×3 m=24 m2\text{Area}_1 = 8 \text{ m} \times 3 \text{ m} = 24 \text{ m}^2 Area2=5 m×2 m=10 m2\text{Area}_2 = 5 \text{ m} \times 2 \text{ m} = 10 \text{ m}^2

  3. Add the areas of the two rectangles to find the total area.

    Total Area=Area1+Area2=24 m2+10 m2=34 m2\text{Total Area} = \text{Area}_1 + \text{Area}_2 = 24 \text{ m}^2 + 10 \text{ m}^2 = 34 \text{ m}^2

    The area of the floor is 34 m2\boxed{\text{34 m}^2\text{}}.

Part iii

GH¢ 680.00\text{GH¢ 680.00}

Cost of carpeting the floor

  1. Use the total area and the cost per square metre.

    The total area is 34 m234 \text{ m}^2 and the carpet cost is GH¢ 20.00 per square metre.

  2. Calculate the total cost.

    Total Cost=Total Area×Cost per square metre\text{Total Cost} = \text{Total Area} \times \text{Cost per square metre} Total Cost=34 m2×GH¢ 20.00/m2\text{Total Cost} = 34 \text{ m}^2 \times \text{GH¢ } 20.00/\text{m}^2 Total Cost=GH¢ 680.00\text{Total Cost} = \text{GH¢ } 680.00

    The cost of carpeting the floor is GH¢ 680.00\boxed{\text{GH¢ 680.00}}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QCalculate the perimeter and area of an L-shaped room with given dimensions.QCalculate the total area of the floor plan shown in the image, assuming all dimensions are in…QFind the perimeter of the plan below.QCalculate the perimeter of the L-shaped figure A and the T-shaped figure B.QFind the area of the L-shaped figure shown below, which is composed of two rectangles.
Browse by topic:Geometry
See all Mathematics questions →
Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp