Answer:
1.
Part 1: Circumference is 11.31 meters
Part 2: Area is 10.18 square meters
2.
Part 1: Backboard's Length = 1.05 meters
Part 2: Perimeter is 187.8 meters
Part 3: Area of seating space is 178 square meters
3. Area is 21 square meters.
4.
Part 1: Perimeter is 255.41 meters
Part 2: Area is 3097.97 square meters.
Step-by-step explanation:
Question 1:
Part 1:
The formula for the circumference of a circle is given by:
[tex]C=\pi d\\C=\pi (2r)\\C=2\pi r[/tex]
Where radius (r) is half of diameter (d)
Since radius of the circle shown in 1.8m, we plug it in the formula and get:
[tex]C=2\pi r\\C=2\pi (1.8)\\C=11.31[/tex]
So C = 11.31 meters
Part 2:
The area of the circle is given by the formula:
[tex]A=\pi r^2[/tex]
Where A is the area and r is the radius
Since we know r = 1.8, we plug it in the formula and find area:
[tex]A=\pi r^2\\A=\pi(1.8)^2\\A=10.18[/tex]
Area is 10.18 sq. meters.
Question 2:
Part 1:
Area of a rectangle is length * width
width is given in 1.8 m, which in cm, is 1.8 multiplied by 100, so we have
[tex]1.8*100=180[/tex]cm
To find Length, we plug area equal to 18,900 and width equal to 180 cm and solve:
[tex]A=length*width\\18,900=length*180\\length=\frac{18,900}{180}\\length=105[/tex]
Length is 105 cm, in meters, we divide by 100, to get [tex]\frac{105}{100}=1.05[/tex]
Backboard's Length = 1.05 meters
Part 2:
Perimeter means the sum of all the sides of the figure (however many sides it might have). If you look at the seating space, it has 8 sides, 4 of the outer sides and 4 of the inner sides. We just add all of them to get the perimeter.
Perimeter = [tex]18.4+32.5+18.4+32.5+15+28+15+28=187.8[/tex]
Thus the perimeter is 187.8 meters
Part 3:
Area of the seating space can be written as:
Area of seating space = area of big rectangle - area of basketball court
Area of big rectangle is length * width = [tex]18.4*32.5=598[/tex]
Area of basket ball court is length * width = [tex]15*28=420[/tex]
Now,
Area of seating space = 598 - 420 = 178 square meters.
Question 3:
Area shape consists of 4 same triangles (with base of 3 and height of 2) & 1 square (with side 3) in the middle.
To get the area of the shape we add area of 4 triangles & area of square.
Area of 1 triangle is
[tex]A=\frac{1}{2}*b*h=\frac{1}{2}*3*2=3[/tex]
Area of 4 of the triangles is
[tex]4*3=12[/tex]
Now, area of square is given by (side * side):
[tex]A=s^2=3^2=9[/tex]
Area of square is 9
Hence, area of shape = 12+9=21 square meters
Question 4:
Part 1:
The perimeter is sum of all the sides of the figure. If we start from left side (4000cm) and go clockwise, we can identify all the sides.
- Starting side is 4000 cm side. 4000cm divided by 100 (to get it into meters): 40 m
- top is 10 m and 68 m = 78 m
- right side is 33 m
- then we have semicircle, since whole circle's circumference (perimeter) is [tex]2\pi r[/tex], semicircle's perimeter is half of that so [tex]\frac{2\pi r}{2}=\pi r=\pi (17)=53.41[/tex]m
- then a side of 34 m (bottom)
- then 700 cm , in meters we divide by 100, so 7m
- then 10 m is the last one before we come to starting point
Perimeter = [tex]40+10+68+33+53.41+34+7+10=255.41[/tex]
Perimeter is 255.41 meters
Part 2:
Area of the figure can be found by dividing the figures. From left, we can see that the whole figure consists of
- Left rectangle with length 40 m and width 10 m. Thus area of rectangle is length * width = 40 * 10 = 400
- Then another rectangle with length 68 m and width 33 m. Thus area of this rectangle is length * width = 68 * 33 = 2244
- Lastly in the bottom we have half a circle, area of whole circle is [tex]\pi r^2[/tex] and that of this semicircle is half of this so area is [tex]\frac{\pi r^2}{2}=\frac{\pi (17)^2}{2}=453.96[/tex]
Adding all these we get the area of the figure:
Area = [tex]400+2244+453.96=3097.96[/tex]
Area is 3097.97 square meters.
