Find the areas of the unshaded regions:
Problem 1 :
Solution :
In the picture given above, we have two rectangles. To find area of unshaded region,
= Area of large rectangle - Area of smaller rectangle
= 9 x 8 - 6 x 3
= 72 - 18
= 54 m2
Problem 2 :
area of unshaded region = Area of large rectangle – area of triangle – area of small rectangle
= l w – (1/2) b h – l w
= 12 x 8 – (1/2) x 6 x 4 – 2 x 8
= 96 – 12 - 16
= 68 cm2
So, area of unshaded region is 68 cm2.
Problem 3 :
Chelsea measures the windows in her flat so she can calculate the length of curtain track that she needs to buy. Her measurements are 1.2 m , 1.2 m , 1.8 m , 90 cm and 45 cm. how many meter of track does Chelsea need ?
Solution :
Given Measurements are, 1.2 m , 1.2 m , 1.8 m , 90 cm and 45 cm
Converting cm to meters.
So , 90 cm = 0. 9 m and 45 cm = 0. 45
Perimeters = sum of the length of its all sides
= 1. 2 + 1. 2 + 1. 8 + 0. 9 + 0. 45
= 5. 55 m
So, Chelsa needs 5.55 m of track.
Problem 4 :
A rug measuring 2.5 m by 3.5 m was places in a room 6.4 m long and 8.2 m wide . what area of floor is not covered by the rug ?
Solution :
Area = l x w
Here , l = 2.5 m and w = 3.5 m
Area of rug = 2.5 x 3.5
A = 8.75 m2
l = 6.4 m and w = 8.2 m
Area of floor = 6.4 x 8.2
A = 52.48 m2
Area of floor is greater than the area of rug. So, rug cannot cover the floor.
To find the area not covered by the rug
= 52.48 - 8.75
= 43.73 m2
Problem 5 :
Solution :
Base of the triangle = 5x+2
Height = 4x
Area of green shaded region = Area of triangle
= (1/2) ⋅ base ⋅ height
= (1/2) ⋅ (5x+2) ⋅ 4x
= 2x(5x+2)
= 10x2 + 4x
Area of shaded region is (10x2 + 4x) m.
Problem 6 :
Solution :
Area of green shaded region = Area of large rectangle - Area of small rectangle
= (x+11) ⋅ 2x - (x+3) ⋅ x
= 2x2+22x-3x2-3x
= -x2+19x
Problem 7 :
Solution :
Area of parallelogram = Base x Height
Base = 3a+5 and height = 4a-3
= (3a+5)(4a-3)
= 12a2-9a+20a-15
= 12a2+20a-15
Problem 8 :
Solution :
Area of circle = πr2
= π(2x)2
= 4πx2
Area of circle is 4πx2.
Problem 9 :
Solution :
Area of shaded region = Area of large square - Area of small square
A = l w – s2
= (x + 5) · (x + 5) – x2
= x2 + 5x + 5x + 25 – x2
A = 10x + 25
Area of shaded region in purple colour is (10x+25) m.
Problem 10 :
Solution :
Area A = area of rectangle + area of semicircle
A = l w + πr2/2
A = 4x · (x+1) + πr2/2
= 4x2 + 4x + π (2x)2/2
= 4x2 + 4x + 4πx2 /2
= 4x2 + 4x + 2πx2
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