Find the perimeter and area of the given Figure. \(\left( \pi =\frac { 22 }{ 7 } \right) \)

Nishanth has a key-chain which is in the form of an equilateral triangle and a semicircle attached to a square of side 5 cm as shown in the Figure. Find its area.(π = 3.14, √3 = 1.732)

Find the area of the irregular polygon field whose measures are as given in the figure.

Divide : (5y³ − 25y² + 8y) by 5y

Factorise : x² + 8x + 16

Factorise: x³ +125

Construct a quadrilateral DEAR with DE = 6 cm, EA = 5 cm, AR = 5.5cm, RD = 5.2 cm and DA = 10 cm. Also find its area.

Construct a quadrilateral MATH with MA = 4 cm, AT = 3.6 cm, TH = 4.5 cm, MH = 5 cm and ∠A = 85°. Also find its area.

There are 3 blue tiles  3 green tiles   and 3 red tiles  Put them together to form a square so that no two tiles of the same colour are adjacent to each other.

Use graph colouring to determine the minimum number of colours that can be used. The adjacent states should not have the same colour.
Use the graph given below such that,
(i) each state is assigned a coloured vertex.
(ii) edges are used to connect the vertices of States.