202k views
4 votes
Write an expression for the area and perimeter for the figure shown

Write an expression for the area and perimeter for the figure shown-example-1
User Glcheetham
by
8.0k points

1 Answer

2 votes

Answer:

Area = 3x² + 7x + 3

Perimeter = 8x + 8

Explanation:

The figure can be decomposed into two: a large rectangle and a smaller rectangle.

✍️Dimensions of the large rectangle:

Length = (x + 1) + x = x + 1 + x = (2x + 1)

Width = (x + 3)

Area = length × width

Area = (2x + 1)(x + 3)

Expand

2x(x + 3) +1(x + 3)

2x² + 6x + x + 3

Area = 2x² + 7x + 3

✍️Dimensions of the large rectangle:

Length = x

Width = x

Area = length × width

Area = x × x = x²

✍️Area of the figure = area of the large rectangle + area of the smaller rectangle

Area of the figure = (2x² + 7x + 3) + x²

Area of the figure = 2x² + x² + 7x + 3

✅Area = 3x² + 7x + 3

✍️ Perimeter of the figure = sum of the length of all sides of the figure = (x + 3) + x + x + x + (x + 1) + (x + 3) + (x + 1) + x

✅Perimeter = 8x + 8

User Mrtechtroid
by
7.9k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories