Math Problem Statement

Find the area of the trapezoid given base 1 = 3/8 yd, base 2 = 7/8 yd, and height = 1/3 yd.

Solution

To determine the area of the given figure, we first identify the shape as a trapezoid.

Trapezoid Area Formula:

The area AA of a trapezoid is given by:

A=12×(b1+b2)×hA = \frac{1}{2} \times (b_1 + b_2) \times h

Where:

  • b1b_1 and b2b_2 are the lengths of the parallel sides (bases),
  • hh is the height of the trapezoid.

Given Measurements:

  1. Base 1 b1=38ydb_1 = \frac{3}{8} \, \text{yd}
  2. Base 2 b2=78ydb_2 = \frac{7}{8} \, \text{yd}
  3. Height h=13ydh = \frac{1}{3} \, \text{yd}

Step 1: Add the Bases

b1+b2=38+78=108=54b_1 + b_2 = \frac{3}{8} + \frac{7}{8} = \frac{10}{8} = \frac{5}{4}


Step 2: Apply the Formula

Substitute the values into the area formula:

A=12×(b1+b2)×hA = \frac{1}{2} \times (b_1 + b_2) \times h

A=12×54×13A = \frac{1}{2} \times \frac{5}{4} \times \frac{1}{3}


Step 3: Simplify

Multiply the fractions step-by-step:

A=151243A = \frac{1 \cdot 5 \cdot 1}{2 \cdot 4 \cdot 3}

A=524yd2A = \frac{5}{24} \, \text{yd}^2


Step 4: Compare to the Options

The given options are expressed in improper fractions. Converting 524\frac{5}{24} to match the closest option, we check:

None of the options match exactly based on my calculation. Please clarify if the values were typed or interpreted differently.

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Math Problem Analysis

Mathematical Concepts

Geometry
Trapezoid Area Calculation
Fractions

Formulas

Area of a trapezoid: A = (1/2) * (b1 + b2) * h

Theorems

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Suitable Grade Level

Grades 6-8