Answer:
See below.
Step-by-step explanation:
So first, we can separate the entire figure into a semi-circle and an isosceles triangle.
AREA:
The area for a semi-circle is [tex]\frac{1}{2}\pi r^2[/tex].
The diameter is 8cm, so the radius is 4cm.
Area of the semi-circle is:
[tex]\frac{1}{2}(4)^2\pi=\frac{1}{2}(16\pi)=8\pi cm^2[/tex]
The area for a triangle is [tex]\frac{1}{2}bh[/tex].
The base is the same as the diameter (8), and we are given the height as 10. Thus:
[tex]\frac{1}{2} (8)(10)=8(5)=40cm^2[/tex]
The total area is [tex](8\pi +40 )cm^2[/tex]
PERIMETER:
The perimeter of a semicircle is: [tex]\pi r + 2r[/tex] (this is derived from dividing the circumference by 2 and then adding on the diameter).
Thus, the perimeter is:
[tex]4\pi +8[/tex]
However, we ignore the 8 since the 8 is not part of the perimeter.
The perimeter of the triangle is the two slant lengths. We know the base and the height, so we can use the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex]
[tex]4^2+10^2=c^2[/tex]
[tex]c^2=116[/tex]
[tex]c=\sqrt{116}=2\sqrt{29[/tex]
Two of them will be [tex]4\sqrt{29}[/tex]
Thus, the total perimeter is [tex]4\pi + 4\sqrt{29}[/tex]
