Questions: In the graph below, each grid square represents one square yard. What is the area of the shaded figure? A 20 yd^2 B 30 yd^2 C 36 y^2

In the graph below, each grid square represents one square yard. What is the area of the shaded figure? A 20 yd^2 B 30 yd^2 C 36 y^2
Transcript text: In the graph below, each grid square represents one square yard. What is the area of the shaded figure? A $20 y d^{2}$ B $30 \mathrm{yd}^{2}$ C $36 y^{2}$
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Solution

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Solution Steps

Step 1: Identify the Shape and Grid

The shaded figure is a quadrilateral, and each grid square represents one square yard.

Step 2: Decompose the Shape

Decompose the quadrilateral into two triangles by drawing a diagonal from one vertex to the opposite vertex.

Step 3: Calculate the Area of Each Triangle

  1. Triangle 1:

    • Base = 6 yards (horizontal distance)
    • Height = 5 yards (vertical distance)
    • Area = 1/2 * base * height = 1/2 * 6 * 5 = 15 square yards

  2. Triangle 2:

    • Base = 6 yards (horizontal distance)
    • Height = 5 yards (vertical distance)
    • Area = 1/2 * base * height = 1/2 * 6 * 5 = 15 square yards

Final Answer

The area of the shaded figure is the sum of the areas of the two triangles: \[ 15 \text{ square yards} + 15 \text{ square yards} = 30 \text{ square yards} \]

The correct answer is: \[ \boxed{30 \text{ yd}^2} \]

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