Find the value of x.

The lengths of two adjacent sides of a parallelogram are respectively 51cm and 37cm. If one of its diagonal is 20cm then find the area of the parallelogram.

Find the area of the shaded region. Here ABC is an equilateral triangle of side 14cm and BDC is a semicircle.
 

If △ BCD = △ OPQ, △ OPQ ≅ △ TUV , then what is the relation between △ BCD and △
TUV ?

In the complex number system, what is the value of  ? (Note:

Note:
It is advised to memorize the values of powers of i , that is ,

We can observe that   for all natural number . Also, even powers of  is always a real number n, either 1 or - 1

Use coordinate notation to describe the translation.
16 units to the right, 7 units up

Find the values of x, y and z.
 

Use coordinate notation to describe the translation.
5 units to the left, 5 units down

Name the type of transformation shown.

Rotations preserve distances from the _____

Find the area of the trapezium ABCD with the given values.

The endpoints of 𝐴𝐵 are A (100, -111) and B
(222, 525). A reflection of 𝐴𝐵 results in the image 𝑋𝑌, with coordinates X (-100, -111) and Y (-222, 525). Tell which axis 𝐴𝐵 was reflected in and write the coordinate rule for the reflection.

The endpoints of 𝑀𝑁 are M (7, 9) and N (2, 5). A reflection of 𝑀𝑁 results in the image 𝑆𝑇, with coordinates S (7, -9) and T (2, -5). Tell which axis 𝑀𝑁 was reflected in and write the coordinate rule for the reflection.

The vertices of △ 𝑃𝑄𝑅 are P (1, 0), B (5, 5), and C
(5, 0). A translation of results in the image △ 𝐿𝑀𝑁 with vertices L (-1, 3), M (3, 8), and N (3, 3). Describe the translation in words and in coordinate notation.

The vertices of △ 𝐴𝐵𝐶 are A (2, 4), B (1, 1), and C (5,1). A translation of △ 𝐴𝐵𝐶 results in the image △𝑃𝑄𝑅 with vertices P (3, 2), Q (2, -1), and R (6, -1). Describe the translation in words and in coordinate notation.

Use a reflection in the x – axis to draw the other half of the pattern.