Rs 55

Given, dimensions of cuboid are 60 cm\(\times\)54 cm\(\times\)30 cm
i.e.length= 60 cm, breadth = 54 cm and height = 30 cm
∴ Volume of the cuboid = l \(\times\)b \(\times\)h = 60\(\times\)54 \(\times\)30
 = (60\(\times\)54\(\times\)30)cm³
Also,givenside of a small cube = 6 cm
∴ Volume of one cube = a³ = (6)³ = (6\(\times\)6 \(\times\)6) cm³
Here,small cubes are placed in cuboid, required number of smallcubes
=\(\frac { Volume\ of\ cuboid }{ Volume\ of\ one\ cube } =\frac { 60\times 54\times 30 }{ 6\times 6\times 6 } \)  = 450

Given,base area of cuboid = 180 cm²
and volume of cuboid = 900 cm³
We know that, volume of cuboid = Base area\(\times\) Height
⇒ 900 = 180 Heigth ⇒ Height = \(\frac { 900 }{ 180 } \)=5 cm
Hence,height of the cuboid is 5 cm.

∴  VoIume of the cylinder =  \({ \pi r }^{ 2 }h=\frac { 22 }{ 7 } \times 7\times 7\times 10\)=1540 cm³

Given, side of cube = 1.5 cm
∴ Volume of the cube = 1.5 =l³ = (1.5)³ = 1.5\(\times\)1.5\(\times\)1.5 = 3.375 m³

1050 m²

 In the given figure, we have 24 cubes, which have 1 face painted.

Given,length (1)= 4 cm, breadth (b) = 4 cm and and height (h) = 10 cm
∴ Total surface area of the cuboid = 2(lb+ bh + hl)
2(4\(\times\)4+4\(\times\)10+10\(\times\)4) = 2(16 + 40 + 40) = 2 \(\times\)96 = 192 cm²

30100 m²

Given, area of trapezium = 34 cm²
and height of trapezium = 4 cm
Let length of one parallel side be x cm, then another parallel side is 10 cm.
Now, area of trapezium =\(\frac { 1 }{ 2 } \times \) sum of parellel sides\(\times\)Perpendicular distance between the parallel sides
⇒  34 =\(\frac { 1 }{ 2 } \times \) (x+10) \(\times\)4 ⇒ 34 =2x(x+10)
⇒ 17 = x + 10
⇒ x = 17-10 = 7
Hence, the length of other parallel side is 7 cm

In a parallelogram, opposite sides are parallel and equal, so by drawing a diagonal, it can be divided into two congruent triangle but in a trapezium, only one pair of opposite sides is parallel, so it cannot be divided into two congruent triangles

Area of polygon ABCD = Area of ΔABP +Area of trapezium BCSP+Area of ΔCDS
= \(\frac { 1 }{ 2 } \)\(\times\)AP \(\times\)PB + PS \(\times\)(PB+SC)+ SD\(\times\) SC
= \(\frac { 1 }{ 2 } \)\(\times\)2\(\times\) 2+\(\frac { 1 }{ 2 } \)\(\times\)5 (2+3)+ 3\(\times\) 3
 =2 +12.5+4.5 = 19cm²
Hence the area of polygon ABCD is 19 cm²

We have d₁ =20cm d₂ =15 cm
Area of rhombus =\(\frac { 1 }{ 2 } \) \(\times\)d₁ \(\times\)d₂ = \(\frac { 1 }{ 2 } \)\(\times\)20 \(\times\)15 = \(\frac { 1 }{ 2 } \)\(\times\)300 = 150 cm²
Hence, the area of rhombus 150 cm²

240 m²

400 m²