Respuesta :
Finding the lengths of the legs of the right triangle, we have 6 and 3. (6*3)/2 = 9. Finding the area of the semi-circle we obtain [tex]\frac{1.5^2\pi}{2} [/tex] which rounding to 3.14 as pi, we obtain 3.5325. Adding up the area of the triangle and the semi-circle and the triangle we get 9+3.5325 which equals 12.5325
The area of the figure that is made up of a triangle and a semicircle is 23.137 units².
What is the area of a triangle?
The area of a triangle is half the product of its base and its height.
[tex]Area \triangle = \dfrac{1}{2}\times base \times height[/tex]
In order to solve the problem, we will divide the given figure into two parts such that the first one will be a right-angled triangle while the second one is a semi-circle as shown below.
As we can see in the ΔABC, the height of the triangle is 3 units, while the length of the base of the triangle is 6 units. therefore, the area of the triangle can be written as,
[tex]\begin{aligned}\triangle ABC &= \dfrac{1}{2} \times height \times base\\\\&= \dfrac{1}{2} \times BC \times AB\\\\& = 0.5 \times 3 \times 6\\\\& = 9\rm\ unit^2 \end{aligned}[/tex]
Now, if we look at the semi-circle we will find that the diameter(BC) of the semi-circle is 3 units, therefore, the area of the semi-circle can be written as,
[tex]\begin{aligned}\text{Area of Semi-circle} &= \dfrac{\pi}{2}d^2\\\\ &= \dfrac{\pi}{2}(3)^2\\\\&= 14.137\rm\ units^2 \end{aligned}[/tex]
Further, in order to get the total area of the figure, simply add the two areas, therefore,
The area of the figure = Area of triangle + Area of the semi-circle
= 9 + 14.137
= 23.137 units²
Hence, the area of the figure that is made up of a triangle and a semicircle is 23.137 units².
Learn more about Area of Triangle:
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