Math Problem Statement

Find the area of various quadrilaterals based on the given worksheet, which includes squares, rectangles, trapezoids, parallelograms, and rhombuses.

Solution

It seems you've uploaded an image of a worksheet with various quadrilaterals, and you're tasked with calculating the areas. I can guide you through how to solve each one.

To proceed, let's break down the shapes and formulas used for calculating the area of each quadrilateral:

  1. Square/Rectangle (Shape 1): The formula for area is Area=side2\text{Area} = \text{side}^2 for squares, and Area=length×width\text{Area} = \text{length} \times \text{width} for rectangles.
  2. Trapezoid (Shape 2, Shape 7, Shape 8, Shape 9): The formula for area is Area=12×(a+b)×h\text{Area} = \frac{1}{2} \times (a + b) \times h, where aa and bb are the lengths of the parallel sides, and hh is the height (perpendicular distance between the parallel sides).
  3. Parallelogram (Shape 3): The formula for area is Area=base×height\text{Area} = \text{base} \times \text{height}.
  4. Rhombus (Shape 4): The formula for area is Area=12×d1×d2\text{Area} = \frac{1}{2} \times d_1 \times d_2, where d1d_1 and d2d_2 are the diagonals.

Let me know if you'd like me to solve any specific shape or if you'd prefer a step-by-step calculation for any of these!

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Math Problem Analysis

Mathematical Concepts

Geometry
Area Calculation
Quadrilaterals

Formulas

Area of square: side × side
Area of rectangle: length × width
Area of trapezoid: 1/2 × (a + b) × h
Area of parallelogram: base × height
Area of rhombus: 1/2 × d1 × d2

Theorems

Pythagorean theorem (if diagonal dimensions are required)

Suitable Grade Level

Grades 6-8