Question

Write an expression for the area and perimeter for the figure shown

Answer 1

Answer:

Area = 3x² + 7x + 3

Perimeter = 8x + 8

Step-by-step 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