Question 11
Question: Find the area of the quadrilateral ABCD in which AB = 14 cm, BC = 24 cm, CD = 24 cm, AD = 18 cm, AC = 30 cm.
Answer:
In ABC,
= 40 x 4.12
= 164.8 cm2
in ACD,
Area of the quadrilateral = 164.8 + 216 = 380.8 cm2
Question 12
Question: Find the area of a quadrilateral ABCD whose sides are 9m, 40 m, 28 m and 15 m respectively and the angle between the first two sides is a right angle.
Answer:
AC2 = AB2 + BC2 = 81 + 1600 = 1681
Therefore AC= 41 m
Area of ABC 
= 126 m2
Area of the quadrilateral = 180 + 126 = 306 m2
Question 13
Question: A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.
Answer:
Let us draw BE || AD
Then ABED is a parallelogram BE = 13 m DE = 10 m EC = 15 m
For BEC,
Height of trapezium = 11.2 m
Area of field
= 196 m2
Question 14
Question: The perimeter of a right triangle is144 cm and its hypotenuse measures 65 cm. Find the length of the other sides and calculate its area. Verify the result using Hero's formula.
Answer:
a + b + 65 = 144 a + b = 79 ... (1)
a2 + b2 = 652 (Pythagoras theorem)
= 4225
Squaring (1) (a + b)2 = 792 = 6241
2ab = 6241 - 4225 = 2016
(a - b)2 = a2 + b2 - 2ab
= 4225 - 2016 = 2209
a + b = 79
a - b = 47
2a = 126
a = 63
b = 16
Hero's Formula
= 504 cm2
Hence verified.
Question 15
Question: At the centre of a floor there is a pattern made of 8 triangular tiles of the same size. The shaded portions are made of green tiles and the rest are while. The sides of the tiles are 19.5 cm, 21 cm, 22.5 cm respectively. The cost of the green tiles is Rs.30/100 cm2 and the cost of the white tiles is Rs.25/100 cm2 and the cost of the white tiles is Rs.25/100 cm2. What is the cost of making the pattern?
Answer:
The areas of all the triangles are equal.
The semi perimeter of one
= 31.5
= 108 cm2
Area of 4 green tiles = 108 x 4 = 432 cm2
The cost of green tiles = 4.32 x 30 = Rs. 129.60
|||ly Cost of white tiles = 4.32 x 25 = Rs. 108
Total cost = Rs. 237.60
Question 16
Question: Two adjacent sides of a parallelogram measure 15 cm and 10.5 cm. One of its diagonal measures 19.5 cm. What is the area of the parallelogram. Find the length of the altitude drawn to the longer side.
Answer:
Semi perimeter of ABC
Area of the parallelogram
Area of parallelogram = b x h = 15 x DP
Therefore 
Question 17
Question: A trapezium has parallel sides of lengths 9 cm and 5 cm. The other two sides are of length 2.5 cm. Find its area
Answer:
BE is drawn || AD
ADEB is a parallelogram DE = 5 cm EC = 4 cm
BE= 2.5 cm
Semi perimeter of BEC 
Question 18
Question: A field is in the shape of a rhombus with each side 75 m and one of its diagonals is 42 m. If a man working in the field can level 63 m2 of the field in one day and there are 4 men working how many days will they take to level the field?
Answer:
Semi perimeter of ABD
= 4 x 6 x 21 x 3
= 1512 m2
Area of field = 1512 x 2 = 3024 m2
Area of field which 4 men can level in 1 day = 63 x 4 = 252 m2
Number of days they need to level the field
Question 19
Question:
This is a model of an aeroplane, made of colour paper. Find the total area of the paper used.
Answer: ABC is an isosceles triangle with sides 5 cm, 5 cm, 1 cm
Part II is the rectangle BCGH with sides 1 cm and 6.5 cm long.
Area of II = 1 x 6.5 = 6.5 cm2
Part III HGIJ is a trapezium
Area of equilateral GKI 
IV and V are right angled triangles each with area
Therefore total area = 2.3 + 6.5 + 1.3 + 4.5 + 4.5
= 19.1 cm2
Question 20
Question: An umbrella is made by stitching 10 triangular pieces of cloth of two different colours, each piece measuring 20 cm, 50 cm, 50 cm. How much cloth of each colour is used in the umbrella?
Answer:
Semi-perimeter of each triangle
Area of 1 triangle 
Area of cloth of each colour = 5 x 490 cm2
= 2450 cm2
