In this lesson, let’s learn how to compute area and parameters of complex figures. We’re given two problems. I'm going to do the first one first. We need to find the area and the parameter of the complex figure given to us. As we can see this is a semi-circle, half a circle and this is a triangle.
So the are of the figure is area of the semi-circle plus area of the triangle, lets compute them separately. What's area of the semi-circle, well its half the area of the semi-circle, right. Which is ½ π*r² which is the area of a full circle, you just half that, which is 1/2* π* do we know the radius. Well the radius of this circle, if this height of this triangle is 6cm, radius is half that so its 3cm*3², cm² is the unit, which is 9/2*π. Which is we take π as 3.14 we get the area is 9*3.14/2cm². If I multiply this we get 14.13cm², that’s the area of the semi-circle, I'm just drawing the semi-circle instead of writing the whole thing down.
Area of the triangle is simple, ½*base which is 8cm* the height which is 6cm, okay. Which is 8*6 is 48/2 is 24cm², so the final area we are looking for is 14.13+14 which is 38.13cm² that’s the area of this complex figure, okay. Now when want to find the Circumference, circumference is the sum of all the sides which is this part. So half of the Circumference of a circle, half of the Circumference of a circle plus length of this two sides which is 18cm, 10 and 8. Circumference of the circle is π*diameter which is 6cm+18cm and this is multiplied by half, which is ½ or 3*π 6/2 is three*π+18cm. which is 3* π is 9.42+18cm, 18+9.42 is 27+.42cm that’s the Circumference of this complex figure.
Relatively easy to do, keeping to remember is the Circumference of half a circle is half of the Circumference of the entire circle, π*d. Now lets look at the second problem, we need to find the area of the shaded region. Well the area of the shaded region equals area of the rectangle minus area of the semi-circle *2 because there are two of them exactly the same measurements.
So what is the area of the rectangle, well the dimensions are 20ft by 10ft so its 20*10²ft or 200²ft, that’s easy. Area of the semi-circle is ½*π*radius² ½ because it’s half the area of the circle. Area of the circle is π*radius square, what's the radius. If the height is 10ft and the center of the circle is here, the radius is 5ft. So area of the half a circle is 1/2*π which is 3.14*5ft² or 25²ft 5*5 is 25. When I multiply this, area of half a circle becomes ½*3.14*25 or it is 101.57*25ft², that’s the area of half the circle but we need twice that. So 2*area of half circle equals 1.57*25*2ft², all I did was multiply the area of ½ one semi-circle with two to get both this areas. So area of two semi-circles equals, if I multiply 1.57*2*25 we get 78.5²ft. So area of the two semicircles is 78.5, area of the rectangle is 200, let’s circle those. Area of a rectangle is 200, area of the two semi-circles is 78.5, so the final area of the shaded figure is 200-78.5²ft which is 122.5²ft. That’s the answer we are looking for.
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