Math Problem Statement

Show my work

Calculate the perimeter and area of a rectangle with a length of 36.5 meters and a width of 40.5 meters. Show your work.

Solution

In this image, you're working on calculating the perimeter and area of a rectangle.

Given:

  • Length: 36.5 m
  • Width: 40.5 m

Perimeter Calculation:

The formula for the perimeter PP of a rectangle is:

P=2×(Length+Width)P = 2 \times ( \text{Length} + \text{Width} )

Substitute the values:

P=2×(36.5+40.5)=2×77=154mP = 2 \times (36.5 + 40.5) = 2 \times 77 = 154 \, \text{m}

Area Calculation:

The formula for the area AA of a rectangle is:

A=Length×WidthA = \text{Length} \times \text{Width}

Substitute the values:

A=36.5×40.5=1478.25m2A = 36.5 \times 40.5 = 1478.25 \, \text{m}^2

Summary:

  • Perimeter: 154 m
  • Area: 1478.25 m²

Do you have any other questions or need further clarification?

Here are 5 questions to extend your learning:

  1. How does the perimeter change if both dimensions are doubled?
  2. What is the diagonal length of this rectangle using the Pythagorean theorem?
  3. How do you calculate the area of a square, and how is it different from a rectangle?
  4. Can you derive the formula for the perimeter of any polygon?
  5. How would the perimeter and area change if the length and width were given in centimeters?

Tip: Always double-check units, especially in area calculations, to avoid conversion mistakes.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Geometry
Perimeter
Area

Formulas

Perimeter of a rectangle: P = 2 × (Length + Width)
Area of a rectangle: A = Length × Width

Theorems

-

Suitable Grade Level

Grades 5-6