Three figures are a mixture of the main squares, rectangles, triangles, and trapeziums.
To Find,
The area is enclosed by the figures.
Solution,
(i)For the first figure, it is a figure consisting of a triangle and a square of 4 cm each side.
The area of the triangle is \frac{1}{2} 21
× 4× 2=4 cm^{2}cm 2 .
The area of square with a length of 4 cm each side, is 4×4= 16 cm^{2}cm 2
.
So the total area of the figure is 16+4=20 cm^{2}cm 2
ii)For the second figure, it is a figure consisting of a trapizium with height of 8 cm,parallel sides of 7cm,18cm and a square of 18 cm each side.
Atfirst the area of square is 18×18= 324 cm^{2}cm 2
area of trapezium = \frac{a+b}{2} 2
a+b ×h.
= \frac{18+7}{2} 218+7
× 8.cm^{2}cm 2
=100 cm^{2}cm 2 .
So the total area is
= 324+100=424 cm^{2}cm 2.
iii) For the third figure, it is a figure consisting of a trapizium with height of (28-8)cm=8 cm,parallel sides of 6cm,15cm and a rectangle of 20 cm and 15 each side.
Area of rectangle=(Height×Breadth)=(20×15)=300cm^{2}cm
2
Similarly using the formula ,
Area of trapizium is= \frac{15+6}{2} 2
15+6 ×8 cm^{2}cm 2
=84cm^{2}cm 2Total area of the figure = Area of rectangle+Area of trapizium=300+84=384cm^{2}cm
Answers & Comments
Answer:
Given,
Three figures are a mixture of the main squares, rectangles, triangles, and trapeziums.
To Find,
The area is enclosed by the figures.
Solution,
(i)For the first figure, it is a figure consisting of a triangle and a square of 4 cm each side.
The area of the triangle is \frac{1}{2} 21
× 4× 2=4 cm^{2}cm 2 .
The area of square with a length of 4 cm each side, is 4×4= 16 cm^{2}cm 2
.
So the total area of the figure is 16+4=20 cm^{2}cm 2
ii)For the second figure, it is a figure consisting of a trapizium with height of 8 cm,parallel sides of 7cm,18cm and a square of 18 cm each side.
Atfirst the area of square is 18×18= 324 cm^{2}cm 2
area of trapezium = \frac{a+b}{2} 2
a+b ×h.
= \frac{18+7}{2} 218+7
× 8.cm^{2}cm 2
=100 cm^{2}cm 2 .
So the total area is
= 324+100=424 cm^{2}cm 2.
iii) For the third figure, it is a figure consisting of a trapizium with height of (28-8)cm=8 cm,parallel sides of 6cm,15cm and a rectangle of 20 cm and 15 each side.
Area of rectangle=(Height×Breadth)=(20×15)=300cm^{2}cm
2
Similarly using the formula ,
Area of trapizium is= \frac{15+6}{2} 2
15+6 ×8 cm^{2}cm 2
=84cm^{2}cm 2Total area of the figure = Area of rectangle+Area of trapizium=300+84=384cm^{2}cm
2.Hence, The area of figure (i) is 20cm^{2}cm
2 .(ii) is 424cm^{2}cm
2.(iii) is 384cm^{2}cm2
.