Q1) The diagonal of a rectangle is 25 meters long and makes an angle of 36 degree with one side of the rectangle. Find the area and the perimeter of the rectangle.
Q2) A side of a square is 16 inches. The midpoints of its sides are joined to form an inscribed square. Another is drawn in such a way that its vertices would lie also at the midpoints of the sides of the second square. This process is continued infinitely. Find the sum of the areas of these infinite squares.
Q3) A rectangle and a square have the same area. If the length of the side of the square is 6 units and the longest side of the rectangle is 5 more than the measure of the shorter side. Find the dimensions of the rectangle.
Q4) Find the height of a parallelogram having sides 10 and 20 inches, and an included angle of 35 degree. Also, calculate the area of the figure.
Q5) A certain city block is in the form of a parallelogram. Two of its sides measure 32 ft. and 41 ft. If the area of the land in the block is 656 square feet, what is the length of its longer diagonal?