Let, the length of the required side be ‘x’ cm.
Then, area of the trapezium = \(\cfrac { 1 }{ 2 } \times h\left( a+b \right) sq.units\)
= \(\cfrac { 1 }{ 2 } \times 16(25+x)\)
= 200 + 8x
But, the area of the trapezium = 352 sq. cm (given)
Therefore, 200 + 8x = 352
\(\Rightarrow\) 8x = 352 – 200
\(\Rightarrow\) 8x = 152
 \(\Rightarrow\) \(x=\cfrac { 152 }{ 8 } \)
x = 19
Therefore, the length of the other side is 19 cm.

Given, height (h) = 14 cm
parallel sides are (a) = 18 cm and (b) = 9 cm
Area of the trapezium = \(\cfrac { 1 }{ 2 } \times h(a+b)\)
= \(\cfrac { 1 }{ 2 } \times 14\left( 18+9 \right) \)
= 7(27)
= 189 sq. cm
Therefore, area of the trapezium is 189 sq. cm.

Given: Area = 368 sq. cm , base b = 23 cm
Area of the parallelogram = 368 sq. cm
b × h = 368
23 × h = 368
\(h=\cfrac { 368 }{ 23 } \)
Thus, the height of the parallelogram = 16 cm.

d₁ = 4 cm, d₂ = 5 cm
Area of sweet (rhombus) \(=\frac{1}{2} \times\left(d_{1} \times d_{2}\right) \text { sq.units } \)
\(=\frac{1}{2} \times(4 \times 5)\)
= 10 sq.cm
Area of aluminium foil = Area of 400 sweets
= 400 x 10 sq.cm
= 4000 sq. cm
Cost of aluminum foil per 100 sq.cm = Rs. 7
Cost of aluminum foil for 4000 sq.cm
\(=\frac{7}{100} \times 4000\)
Cost of aluminum foil used for 400 sweets
= Rs. 280

Given base b = 14 cm ; Height h = 9 em
Area of the rhombus = b x h sq. units
= 14 x 9
Area of rhombus = 126 sq.cm

h = 14 m,b = 14 + 8 = 22 m
Area of ground (parallelogram) = b x h sq.units
= 22 x 14 = 308 m²
Cost of levelling the ground = Rs. 15  per sq.m
Cost of levelling the ground = 308 x 15 = Rs. 4620

Given, the length of the diagonals of a rhombus shaped tile are 40 cm and 25 cm
The area of one tile = \(\cfrac { 1 }{ 2 } \times \left( { d }_{ 1 }\times { d }_{ 2 } \right) sq.units\)
= \(\cfrac { 1 }{ 2 } \times 40\times 25\)
= 500 sq.cm
Therefore, the area of 200 such tiles = 200 x 500
= 100000 sq. cm
= \(\cfrac { 100000 }{ 10000 } \)(1sq.m = 1000 sq.cm)
= 10 sq.m
Therefore, the cost of polishing 200 such tiles at the rate of Rs 45 per sq. cm
= 10 x 45 = Rs. 450.

Base = 17 cm, height = 8 cm
Area of the rhombus = b x h sq. units
= 17 x 8 = 136
Therefore, area of the rhombus = 136 sq. cm