**Geometry Problem: Area Calculation****Problem 7:****a.** Determine the areas (in square units) of the 4 lightly shaded triangles in Figure 12.53. The grid lines are 1 unit apart. Explain your reasoning.**b.** Use the moving and additivity principles and your results from part (a) to determine the area of the dark shaded quadrilateral in Figure 12.53. Explain your reasoning.---**Figure 12.53***Four triangles and a quadrilateral forming a rectangle.* **Explanation of the Diagram:**- The provided figure is a geometric diagram consisting of a rectangle that is divided into four lightly shaded triangles and one dark shaded quadrilateral.- The entire figure sits on a coordinate grid with lines spaced 1 unit apart, making it easier to calculate the areas of shapes within the grid.- The total diagram forms a rectangle with its vertices lying on the grid points. Four triangles are positioned at the corners, surrounding a central quadrilateral. **Answer to Part (a):**1. Select one of the lightly shaded triangles to calculate its area.2. Use the formula for the area of a triangle: \( \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} \).3. Given the grid lines are 1 unit apart, measure the base and the height in units by counting the grid squares.**Answer to Part (b):**1. To find the area of the dark shaded quadrilateral, calculate the area of the entire rectangle first.2. Sum the areas of the 4 triangles from part (a).3. Subtract the combined area of the triangles from the area of the rectangle to get the area of the quadrilateral.*Note*: Detailed calculation steps are required for accurate reasoning.This analysis helps to build a foundational understanding of calculating areas using the principles of geometry and the properties of shapes on a grid.

Answered: Image /qna-images/answer/8f48a217-eac8-4ba2-ad5e-6b01c26c668e.jpg

7. a. Determine the areas (in square units) of the 4 lightly shaded triangles in Figure 12.53. The grid lines are 1 unit apart. Explain your rea- soning. b. Use the moving and additivity principles and your results from part (a) to determine the area of the dark shaded quadrilateral in Fig- ure 12.53. Explain your reasoning.

7. a. Determine the areas (in square units) of the 4 lightly shaded triangles in Figure 12.53. The grid lines are 1 unit apart. Explain your rea- soning. b. Use the moving and additivity principles and your results from part (a) to determine the area of the dark shaded quadrilateral in Fig- ure 12.53. Explain your reasoning.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter8: Areas Of Polygons And Circles

Section8.2: Perimeter And Area Of Polygons

Problem 31E: Mary Frances has a rectangular garden plot that encloses an area of 48 yd2. If 28 yd of fencing are...

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