Solid Mensuration
1.) 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.
2.) 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.
3.) 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.
4.) 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.
5.) 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?
6.) The area of an isosceles trapezoid in 246 square meter. If the height and the length of one of its congruent sides measure 6 meter and 10 meter respectively, find the two bases.
7.) An isosceles trapezoid has an area of 40 square meters and an altitude of 2 meters. Its two bases have ratio of 2 is to 3. What are the lengths of the bases and one diagonal of the trapezoid?
8.) A piece of wire of length 52 meters is cut into two parts. Each part is then bent to form a square. It is found that the combined area of thee two squares is 109 square meter. Find the sides of the two squares.
9.) A rhombus has diagonals of 32 and 20 inches. Find the angle opposite the longer diagonal. Also, determine its area.
10.) If you double the length of the side of a square, by how much do you increase the area of that square?
11.) If the diagonal length of a square is tripled, how much is the increase in the perimeter of that square?
2.) 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.
3.) 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.
4.) 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.
5.) 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?
6.) The area of an isosceles trapezoid in 246 square meter. If the height and the length of one of its congruent sides measure 6 meter and 10 meter respectively, find the two bases.
7.) An isosceles trapezoid has an area of 40 square meters and an altitude of 2 meters. Its two bases have ratio of 2 is to 3. What are the lengths of the bases and one diagonal of the trapezoid?
8.) A piece of wire of length 52 meters is cut into two parts. Each part is then bent to form a square. It is found that the combined area of thee two squares is 109 square meter. Find the sides of the two squares.
9.) A rhombus has diagonals of 32 and 20 inches. Find the angle opposite the longer diagonal. Also, determine its area.
10.) If you double the length of the side of a square, by how much do you increase the area of that square?
11.) If the diagonal length of a square is tripled, how much is the increase in the perimeter of that square?