Answer :
Answer:
1)121.5 sq.yards
2)157.92 m²
3)5.434 ft²
4)147.4513 cm²
5)147 cm²
6)56 in²
Step-by-step explanation:
1) Area of shaded region= Area of rectangle-Area of triangle
Area of rectangle= Length*Breadth=18*9 sq.yards=162 sq.yards(length=18 yards and breadth=9 yards)
Area of triangle= [tex]\frac{1}{2}*Base*Height[/tex]=[tex]\frac{1}{2}*9*9[/tex]=40.5 sq.yards(base=9 yards and height= 9 yards)
Therefore,Area of shaded region=162-40.5=121.5 sq.yards
2) In the following figure,
Length of rectangle, l= 21 m
breadth of rectangle, b= 15 m
Radius of circles, r= 5 m
Area of rectangle=l*b=21*15=315 m²
Area of circle= π[tex]r^{2}[/tex]=π*[tex]5^{2}[/tex]=78.54 m²
Therefore,Area of shaded region= Area of rectangle-2*Area of circle
=315-2*78.54=157.92 m²
3) In the following figure,
Radius of circle, r= 2 ft
Base of triangle, b= 6 ft
Height of triangle, h=6 ft
Area of circle= π[tex]r^{2}[/tex]=π*[tex]2^{2}[/tex]=12.566 ft²
Area of triangle= [tex]\frac{1}{2}*Base*Height[/tex]
=[tex]\frac{1}{2}*6*6[/tex]=18 ft²
Therefore,Area of shaded region= Area of triangle- Area of circle
= 18-12.566=5.434 ft²
4) In the following figure,
Radius of circle, r= 6 cm
Length of rectangle, l= 17 cm
breadth of rectangle, b= 2*r= 12 cm
Area of semi-circle= π[tex]\frac{r^{2}}{2}[/tex]=π*[tex]\frac{6^{2}}{2}[/tex]
=56.5487 cm²
Area of rectangle=l*b=17*12=204 cm²
Therefore,Area of shaded region= Area of rectangle- Area of semi-circle
= 204-56.5487=147.4513 cm²
5) In the following figure,
Side of bigger square, a=14 cm
Side of smaller square, b=7 cm
Area of bigger square= [tex]a^{2}[/tex]=[tex]14^{2}[/tex]=196 cm²
Area of smaller square= [tex]b^{2}[/tex]=[tex]7^{2}[/tex]=49 cm²
Therefore,Area of shaded region= Area of bigger square- Area of smaller square
=196-49=147 cm²
6) In the following figure,
Length of rectangle, l= 10 in
breadth of rectangle, b= 8 in
Base of triangle, b= 8 in
Height of triangle, h=6 in
Area of rectangle=l*b=10*8=80 in²
Area of triangle= [tex]\frac{1}{2}*Base*Height[/tex]
=[tex]\frac{1}{2}*8*6[/tex]=24 in²
Therefore,Area of shaded region= Area of triangle- Area of circle
= 80-24=56 in²