The area of the figure is 41.12 square units.
What is the area of the triangle?
The area of the triangle is calculated by half of the product of the height and base of the triangle.
A=(1/2)*height*base
What is the area of the semicircle?
The area of the semicircle can be calculated by the formula given below,
Area of the semicircle= A= πd²/8
where d is the diameter.
Here from the figure, it is clear that the diameter of the semicircle is the distance between the point (-1,0) and (7,0).
diameter=√((7-(-1))²+(0-0)²)=√8²=8 unit
area of the semicircle= πd²/8 = 3.14*8²/8= 25.12 square unit
From the figure, the height of the triangle is the distance between (4,5) and (4,1)
height of the triangle= √(4-4)²+(5-1)²)=√4²=4 unit
the base of the triangle is the distance between the point (-1,0) and (7,0).
the base of the triangle =√((7-(-1))²+(0-0)²)=√8²=8 unit
Area of the triangle= A=(1/2)*height*base= (1/2)*4*8= 16 square units
Area of the whole figure= area of the semicircle+ Area of the triangle =25.12 +16= 41.12 square units
Therefore The area of the figure is 41.12 square units.
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