Math Problem Statement

What is the area and perimeter of a rectangle? How many more cans did one group donate compared to another? What is the missing side and perimeter of a polygon?

Solution

Let's analyze the image. It contains three different tasks:

  1. Thursday Task:

    • A rectangular shape with dimensions 6in6 \, \text{in} and 18in18 \, \text{in}.
    • The goal is to calculate the area and perimeter of the rectangle.
  2. Wednesday Task:

    • A word problem involving canned goods:
      • Third grade donated 98 cans.
      • First grade donated 207 cans.
      • The task is to find how many more cans were donated by the second grade than the third grade.
  3. Tuesday Task:

    • A polygon with labeled and missing sides.
    • The goal is to calculate the missing side and then determine the perimeter.

Let's solve them step-by-step:


Thursday Task (Rectangle):

  • Area: Area=Length×Width=18in×6in=108square inches (sq in).\text{Area} = \text{Length} \times \text{Width} = 18 \, \text{in} \times 6 \, \text{in} = 108 \, \text{square inches (sq in)}.

  • Perimeter: Perimeter=2×(Length+Width)=2×(18in+6in)=2×24in=48in.\text{Perimeter} = 2 \times (\text{Length} + \text{Width}) = 2 \times (18 \, \text{in} + 6 \, \text{in}) = 2 \times 24 \, \text{in} = 48 \, \text{in}.


Wednesday Task (Canned Goods):

  • More Cans: Difference=First Grade DonationThird Grade Donation=20798=109more cans.\text{Difference} = \text{First Grade Donation} - \text{Third Grade Donation} = 207 - 98 = 109 \, \text{more cans}.

Tuesday Task (Polygon):

  • Missing Side: To find the missing side (bottom part), use the total horizontal lengths: Missing Side=21ft(13ft+8ft)=2121=0ft.\text{Missing Side} = 21 \, \text{ft} - (13 \, \text{ft} + 8 \, \text{ft}) = 21 - 21 = 0 \, \text{ft}.

  • Perimeter: Add up all the sides: Perimeter=21ft+13ft+8ft+5ft+13ft+8ft=68ft.\text{Perimeter} = 21 \, \text{ft} + 13 \, \text{ft} + 8 \, \text{ft} + 5 \, \text{ft} + 13 \, \text{ft} + 8 \, \text{ft} = 68 \, \text{ft}.


Let me know if you'd like more details!

Here are 5 related questions to build on this:

  1. What are the formulas for area and perimeter of different polygons?
  2. How can you calculate the area of a composite shape?
  3. How can real-world data (like cans donated) be modeled into equations?
  4. What is the importance of units in geometry problems?
  5. How can subtraction errors impact solving real-world problems?

Tip: Always double-check units and label them in your answers! This ensures clarity and accuracy in mathematical solutions.

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Math Problem Analysis

Mathematical Concepts

Geometry
Arithmetic
Word Problems

Formulas

Area of a rectangle: Length × Width
Perimeter of a rectangle: 2 × (Length + Width)
Perimeter of a polygon: Sum of all sides

Theorems

Properties of rectangles
Properties of polygons

Suitable Grade Level

Grades 3-5