Answer:
41.12 square units
Step-by-step explanation:
You want the area of the attached figure showing a triangle of height 4 atop a semicircle of diameter 8.
Area formulas
The area of a triangle is given by ...
A = 1/2bh
where b is the base and h is the height.
The area of a semicircle is given by ...
A = (π/2)r²
where r is the radius, half the diameter.
Application
The figure shows a triangle with a base of 8 units and a height of 4 units. Its area is ...
A = 1/2(8)(4) = 8·2 = 16
The semicircle has a radius of 4, so its area is ...
A = π/2(4²) = 8π ≈ 25.12
Then the total area of the figure is ...
triangle area + semicircle area = 16 +25.12 = 41.12 square units
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Additional comment
Since the triangle and the semicircle have the same width, we can sum the "equivalent" heights of each and consider the result as a rectangle. You are familiar with the fact that a triangle has half the area of a rectangle the same height, so a triangle of height 4 is equivalent to a rectangle of height 4/2 = 2.
Similarly, the equivalent height of the semicircle can be found to be π/4 times its radius. Here, the radius is 4 units, so the semicircle of diameter 8 is equivalent to a rectangle 8 units by 4(π/4) = π units.
This means the entire figure is equivalent to a rectangle 8 units wide and (2+π) units high. That is the calculation shown in the attachment.
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