The perimeter of the <em>composite</em> figure shown in the figure is equal to 5 · [2 + √2 · (1 + √5)] units (approx. 32.882 units) and the <em>total</em> area is 33.5 square units.
<h3>How to determine the perimeter and the area of a composite figure</h3>
In this case we have a composite figure formed by six triangles and two rectangles. The perimeter is the sum of the <em>side</em> lengths and the area is the sum of the areas of the triangles and rectangles. The perimeter of the entire figure is described below:
p = AB + BC + CD + DE + EF + FG + GA
p = 5√2 + √10 + √10 + 5 + √10 + 5 + 2√10
p = 10 + 5√2 + 5√10
p = 10 + 5 · (√2 + √10)
p = 10 + 5√2 · (1 + √5)
p = 5 · [2 + √2 · (1 + √5)]
And the area of the composite figure is determined by the following expression:
A = 0.5 · (3) · (1) + (3) · (4) + 0.5 · (3) · (1) + 0.5 · (3) · (1) + 0.5 · (3) · (1) + (3) · (2) + 0.5 · (7) · (1) + 0.5 · (6) · (2)
A = 2 · (3) · (1) + (3) · (4) + (3) · (2) + 0.5 · (7) · (1) + 0.5 · (6) · (2)
A = 33.5
The perimeter of the <em>composite</em> figure shown in the figure is equal to 5 · [2 + √2 · (1 + √5)] units (approx. 32.882 units) and the <em>total</em> area is 33.5 square units.
To learn more on composite figures: brainly.com/question/27234680
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