Since opposite sides are parallel, adjacent angles in a rhombus add to 180°.įor finding area, you need to know the height, or altitude, h, of the rhombus. Since opposite angles are equal, and the four angles add to 360°, if you know one angle, you can find all angles. Since the four sides are equal, if you know the length of any side ss, you know the length of all four sides. If you know the length of one side s and the measure of one angle the formula is: a r e a = s 2 sin ( ∠ A ) = s 2 sin ( ∠ B ) area= d 2 only in a square will these be equal-length diagonalsĪltitude, or height – When the rhombus sits with two sides horizontal (flat), the height h is the distance from one side to the opposite side the line segment perpendicular to one side, connecting to the opposite side If you know Altitude (height) and side s the formula is: a r e a = h e i g h t × s area=height\times s a re a = h e i g h t × s The three formulas to find area depend on information you know about the rhombus. The distance from centre of circle to the nearest vertex is 1. There is one using the altitude and side, another using the side and angle, and one for the diagonals. touches all four sides) into rhombus ABCD with one angle 60 degree. If the two acute angles in the rhombus each measure 60. There are three different formulas for finding the area of a rhombus. Answer:Step-by-step explanation:Given a circle is inscribed in a rhombus with sides of length 4 cm. Knowing how to use these measurements can help you find area, perimeter and other facts about the rhombus. The squares of the lengths of the two diagonals are always four times the square of a side.įor such a simple shape, a rhombus has many parts and measurements. These diagonals also bisect each other, which means they divide the rhombus up into four right-angle triangles. Mark off point c as was done when constructing a square. ![]() ![]() Draw a - b and a - d equal in length so that the given angle is angle b - a-d. ![]() One unusual quality of a rhombus is that its diagonals are always perpendicular to each other, no matter the angles of the rhombus's four vertices. 6 To construct a rhombus (figure 18) Figure 20 rhombus trapezium To construct a trapezium when diagonals are given (figure 21) Figure 18 c A rhombus has 01/ its sides and opposite angles equal.
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