Find the area of each of the following figures
Answers
Answer:
i) 99 square units
ii) 36 square units
ii) 24 square units
Step-by-step explanation:
i) The figure(i) shows a trapezium
Area of trapezium = h/2[a + b]
Here h = 9, a = 13 and b = 9
Therefore area = 9/2[13 + 9] = (9 x 22)/2 = 99 square units
ii)To find area of second figure
The figure (ii) shows a rectangle with sides 6 and 5 units and a right angled triangle with base 3 and height 4.
Total area = area of rectangle + area of triangle
To find area of rectangle
Area = length x breadth = 6 x 5 = 30 square units
To find the area of right angled triangle
Area of right angled triangle = 1/ 2x bh =(3 x 4)/2 = 6 square units
To find total area
Total area = area of rectangle + area of triangle = 30 + 6 = 36 square units
iii) To find the area of third figure
This figure also shows one rectangle with length 9 and breadth 1.5 and right angled triangle with base 6(9-3) and height 3.5(5 - 1.5).
To find area of rectangle
Area = length x breadth = 9 x 1.5 = 13.5 square units
To find the area of right angled triangle
Area of right angled triangle = 1/ 2x bh =(6 x 3.5)/2 = 10.5 square units
To find total area
Total area = area of rectangle + area of triangle = 13.5 + 10.5 = 24 squre units
Answer:
Answer of figure (i) 99
figure (ii) 36
figure(iii) 24
Step-by-step explanation:
In figure (i) ABCD is a figure in which ABCE is a square of sides 9 and CED is a right angle triangle
AD = 13
BC = 9
AE = BC = 9
AD - AE =DE
13 - 9 = 4
AB = CE = 9
In Triangle CED
∠E is 90°
DE is a base = 4
CE is a height = 9
Area of Triangle CED = 1/2 * base * height
Area of Triangle CED = 1/2 *4 * 9
= 18
In square ABCE of side 9
Area of Square = (side)^2
Area of Square = (9)^2
= 81
Area of a figure ABCD = Area of a square ABCE + Area of Triangle CED
= 81 +18
= 99
In figure (ii) ABCDE
ABCE is a rectangle of length 6 and breadth 5
Area of rectangle = length * breadth
Area of rectangle = 6 * 5
= 30
In triangle CDE
∠D = 90°
CD is a base of 3
DE is a height of 4
Area of triangle CDE = 1 / 2 * base * height
Area of triangle CDE = 1 / 2 * 3 * 4
=6
Area of Figure ABCDE = Area of ABCE + Area of CDE
= 30 + 6
= 36
In figure (iii) ABCDF
DC = BE = 1.5
AB = 5
AB - BE = AE
5 - 1.5 = 3.5
BC = 9
BC = ED = 9
DF = 3
ED - DF = EF
EF = 6
Area of rectangle BCDE = length * breadth
Area of rectangle BCDE = 9 * 1.5
= 13.5
Area of triangle AEF
EF (base) = 6
AE (height) = 3.5
Area of triangle AEF = 1 / 2 * base * height
Area of triangle AEF = 1 / 2 * 6 * 3.5
= 10.5
Area of Figure ABCDF = Area of rectangle BCDE + Area of triangle AEF
= 13.5 + 10.5
= 24
#SPJ2
