Question

Help plsss brainliest goes to first right answer

Answer 1

Answer:

$Area\ of\ whole\ figure\ = 49.12 ft^2$

Step-by-step explanation:

If we see closely the figure consists of right angled triangle and a semi-circle, so area of the whole figure would be Area of the triangle + Area of the semi-circle so here goes,

We calculate firstly the Area of the triangle,

$Area\ of\ triangle\ =\frac{1}{2}*b*h\\\\Area\ of\ triangle\ =\frac{1}{2}*6*8\\\\Area\ of\ triangle\ =24\ ft^{2}$

Now we calculate the area of the semi-circle,

Semi-circle is also called as Half of a circle, so,

$Area\ of\ a\ circle\ = \pi r^2$

then area of half a circle would be,

$Area\ of\ a\ semi\ circle\ = \frac{\pi r^2 }{2}$

where r is the radius of the circle,

but we don't have the radius we have the diameter which is 8ft to find out the value of radius we divide the diameter by 2 , the formula is:

$d=2r$

where d is the diameter and r is the radius of the circle, so,

$d=2r\\8=2r\\8/2=r\\4=r$

so now we insert the value of radius which is 4ft into the area of a semi-circle,

$Area\ of\ a\ semi\ circle\ = \frac{\pi r^2 }{2} \\\\Area\ of\ a\ semi\ circle\ = \frac{\pi (4)^2 }{2} \\\\Area\ of\ a\ semi\ circle\ = \frac{16\pi }{2} \\\\Area\ of\ a\ semi\ circle\ = 25.12\ ft^2$

Now the Area of the whole figure is

Area of Whole figure = Area of half a circle + Area of triangle

Area of whole figure = 25.12 + 24

Area of whole figure = 49.12 ft^2