Question

Jim says that a 2 1/2 inche by 3 1/4 inch rectangle has a section that is 2 inches x 3 inches and a section that is 1/2 inch x 1/4 inch.That means that area is just the sum of these two smaller areas, or 6 1/8 inches times 2 powers of ten.Why is Jim incorrect?Use an area model to explain your thinking.Then,give the correct area of the rectangle.

Answer 1

multiply the first two numbers then divide

Answer 2

Area of the rectangle is 8¹/₈ in²

Further explanation

To solve the above questions, we need to recall some of the formulas as follows:

Area of Square = (Length of Side)²

Perimeter of Square = 4 × (Length of Side)

Area of Rectangle = Length × Width

Perimeter of Rectangle = 2 × ( Length + Width )

Area of Rhombus = ½ × ( Diagonal₁ + Diagonal₂ )

Perimeter of Rhombus = 4 × ( Length of Side )

Area of Kite = ½ × ( Diagonal₁ + Diagonal₂ )

Perimeter of Kite = 2 × ( Length of Side₁ + Length of Side₂ )

Let us now tackle the problem !

Given:

Length of Rectangle = L = 2¹/₂ in

Width of Rectangle = W = 3¹/₄ in

Unknown:

Area of Rectangle = A = ?

Solution:

This problem is about Area of Rectangle.

$\texttt{Area of Rectangle} = \texttt{Length} \times \texttt{Width}$

$A = L \times W$

$A = 2 \frac{1}{2} \times 3 \frac{1}{4}$

$A = (2 + \frac{1}{2}) \times (3 + \frac{1}{4})$

$A = (2 \times 3) + (\frac{1}{2} \times \frac{1}{4}) + ( 2 \times \frac{1}{4} ) + ( 3 \times \frac{1}{2} )$

$A = 6 + \frac{1}{8} + \frac{1}{2} + \frac{3}{2}$

$A = 6\frac{1}{8} + 2$

$A = \boxed {8\frac{1}{8} ~ \texttt{in}^2}$

Jim is incorrect because he only calculated 2 of the 4 available sections of the rectangle ( as shown in the diagram ).

Learn more

• The perimeter of a polygon : https://brainly.com/question/6361596
• The perimeter of a rectangle : https://brainly.com/question/7619923
• The perimeter of a triangle : https://brainly.com/question/2299951

Answer details

Grade: College

Subject: Mathematics

Chapter: Two Dimensional Figures

Keywords: Perimeter, Area , Square , Rectangle , Side , Length , Width