Free Mensuration Subjective Test 01 Practice Test - 6th grade 

Solution: 1 Mark
Area of the rectangle = length $\times$ breadth

Steps: 1 Mark
Answer: 1 Mark

Area of the given shape = Area of square + Area of rectangle
= (side)${}^2$ + (length $\times$ breadth)

$=(3{)}^2+(2\times 9)=9+18$
 $=27$ sq inches

Steps: 1 Mark
Formula: 1 Mark
Answer: 1 Mark

The perimeter of the blackboard = Length of the steel plate required.

Perimeter of a rectangle $=2\times (L+B)$.

Length of steel plate 

= $2\times (6+5)=2\times 11=22m$

Concept: 1 Mark
Application: 1 Mark
Solution: 1 Mark

$\Rightarrow$ Perimeter = Length of the boundary

= (45 + 22 + 25 + 8 + 20 + (8+22))

= (45 + 22 + 25 + 8 + 20 + (30))

= 150m

$\Rightarrow$ Area of the shape = Area of the larger rectangle + area of smaller rectangle

$=(45\times 22)+(20\times 8)$

$=\left(990\right)+\left(160\right)$

$=1150{cm}^2$

$\therefore$ Area $=1150{cm}^2$

Steps: 1 Mark
Formula: 1 Mark
Answer: 1 Mark

The perimeter of a regular hexagon

= $6\times sidelength$

Perimeter of the hexagon

= $6\times 45feet$

$=270feet$

As they walk 2 rounds:

$\therefore$  Distance covered

= $2\times 270feet$

$=540feet$

Steps: 2 Marks
Formula: 1 Mark
Answer: 1 Mark


Area of the above shapes can be calculated in two steps:
 

i) Area of shape marked 1

ii) Area of shape marked 2

$\Rightarrow$ Area of shape marked 1 = Area of rectangle
= length $\times$ breadth

= 4 $\times$ 9

= 36 cm${}^2$
 

$\Rightarrow$Area of shape marked 2 = Area of triangle

= $\frac{1}{2}\times$ base $\times$ height

= $\frac{1}{2}\times$ 6 $\times$ 4

= 12 cm${}^2$

$\Rightarrow$Area of shape = Area of shape marked 1+ Area of shape marked 2

= (36 + 12) cm${}^2$

= 48 cm${}^2$

Steps: 2 Marks
Formula: 1 Mark
Answer: 1 Mark

Area of one square tile = (side)${}^2$ = (0.5m)${}^2$ = 0.25 m${}^2.$

Area of the kitchen shelf  = length $\times$ breadth

= 4 $\times$ 3 = 12m
 

Number of tiles

= $\frac{\text{Area of kitchen shelf}}{\text{Area of square tile}}$

= $\frac{12}{0.25}$ = 48

Cost of 1 tile = Rs 70

Cost of 48 tiles = Rs 48 $\times$ 70 = Rs 3360

Steps: 2 Marks
Formula: 1 Mark
Answer: 1 Mark

Circumference of a circle

= $2\times \pi \times r=d\times \pi =88inches$

Where, d = diameter  and $\pi =\frac{22}{7}$

$\Rightarrow 88=\frac{22}{7}\times d$

$\Rightarrow d=\frac{88\times 7}{22}$

$\Rightarrow d=28inches$

The diameter of the pizza will be equal to the length of the side of the box.

Side of box = 28 inches

Area of the box = (side)${}^2$  = (28 inches)${}^2$ = 784 inches${}^2$

Each Option: 2 Marks

(a) The above figures can be split into multiple rectangles as follows:


Area of 1st rectangle
$=21\times 7=147c{m}^2$

Area of 2nd rectangle
$=7\times 7=49c{m}^2$

Area of 3rd rectangle
$=7\times 7=49c{m}^2$

Total area of the whole figure
 $=147+49+49=245c{m}^2$


(b) The above figures can be split into multiple rectangles as follows:



Area of 1st rectangle
$=5\times 1=5c{m}^2$

Area of 2nd rectangle
$=4\times 1=4c{m}^2$

Total area of the whole figure
$=5+4=9c{m}^2$