Area of Rhombus
The area of a rhombus is calculated using the formula A = (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals. This formula represents the product of the diagonals divided by 2. The area of a rhombus can also be found using the formula A = base * height, where the base and height are perpendicular to each other.
4 Key excerpts on "Area of Rhombus"
eBook - ePub- Mel Friedman(Author)
- 2012(Publication Date)
- Research & Education Association(Publisher)
...formula where d 1 and d 2 are the diagonals. ABCD is a rhombus. AC = 4 and BD = 7. The area of the rhombus is. • The diagonals of a rhombus bisect the angles of the rhombus. • If the diagonals of a parallelogram are perpendicular, the parallelogram is a rhombus. • If a quadrilateral has four equal sides, then it is a rhombus. • A parallelogram is a rhombus if either diagonal of the parallelogram bisects the angles of the vertices it joins. SQUARES A square is a rhombus with a right angle. • A square is an equilateral quadrilateral. • A square has all the properties of rhombi and rectangles. • In a square, the measure of either diagonal can be calculated by multiplying the length of any side by the square root of 2. • The area of a square is given by the formula A = s 2, where s is the side of the square. • Since all sides of a square are equal, it does not matter which side is used. Example: The area of the square shown below is: A = s 2 A = 6 2 A = 36 The area of a square can also be found by taking the product of the length of the diagonal. squared. This comes from a combination of the facts that the area of a rhombus is d 1 d 2 and that d 1 = d 2 for a square. Example: The area of the square shown below is: TRAPEZOIDS A trapezoid is a quadrilateral with two and only two par allel sides. The parallel sides of a trapezoid are called the bases. The median of a trapezoid is the line joining the midpoints of the nonparallel sides. The perpendicular segment connecting any point in the line containing one base of the trapezoid to the line containing the other base is the altitude of the trapezoid. A pair of angles including only one of the parallel sides is called a pair of base angles. • The median of a trapezoid is parallel to the bases and equal to one-half their sum. • The area of a trapezoid equals one-half the altitude times the sum of the bases, or • An isosceles trapezoid is a trapezoid whose non-parallel sides are equal...
- Sandra Rush(Author)
- 2013(Publication Date)
- Research & Education Association(Publisher)
...A new feature of the parallelogram is that the angles form two pairs, with the ones across from one another being equal. The pairs of adjacent angles add up to 180°, so they are supplementary angles. Rhombus If we add the condition that all four sides of a parallelogram are equal, then we have a rhombus. So a rhombus has all of the properties of a parallelogram plus the sides are equal. Thus, in the above figure of the rhombus, PQ – QR – RS – SP – s, and th e perimeter can be written as Likewise, the area of the rhombus is where any of the sides can be used as the base, and the height drawn to each side is the same. The diagonals of a rhombus bisect each other (as they did for the parallelogram), but now they also are perpendicular to each other. Rectangle If, instead of saying the four sides of the parallelogram are equal, we say that the four angles are equal, we have a rectangle, which is a parallelogram with four equal angles. Thus, in the figure of the rectangle above, and since the angles of a quadrilateral add up to 360°, each of the four angles is 90°, or a right angle. The opposite sides are equal, as in a parallelogram, but not all sides are equal (as they were in the rhombus). The perimeter is written as usual as Because all the angles are right angles, all sides l (length) are perpendicular to sides w (width), so they take the place of the base and height, and the area of the rectangle is If we think of tiling a floor in a straight line, we get an idea of why area is length times width. Suppose we wanted to tile a room that is 12 feet by 10 feet in 1-foot tiles...
eBook - ePub- Surinder Virdi, Roy Baker, Narinder Kaur Virdi(Authors)
- 2014(Publication Date)
- Routledge(Publisher)
...CHAPTER 11 Areas (1) Learning outcomes: (a) Calculate the areas of triangles, quadrilaterals and circles (b) Identify and use the correct units (c) Solve practical problems involving area calculation 11.11 Introduction Area is defined as the amount of space taken up by a two-dimensional figure. The geometrical properties of triangles, quadrilaterals and circles have been explained in Chapter 10. A summary of the formulae used in calculating the areas and other properties of these geometrical shapes is given in Table 11.1. The units of area used in metric systems are: mm 2, cm 2, m 2 and km 2. Table 11.1 Shape Area and other properties Area = l × b Perimeter = 2 l + 2 b = 2(l + b) Area = l × l = l 2 Perimeter = 4 l Area = l × h Area = π r 2 Circumference = 2π r 11.2 Area of triangles There are many techniques and formulae that can be used to calculate the area of triangles. In this section we consider the triangles with known measurements of the base and the perpendicular height, or where the height can be calculated easily. Example 11.1 Find the area of the triangles shown in Figure 11.1. Figure 11.1 Solution: (a) Base BC = 8 cm We need to calculate height AD, which has not been given. As sides AB and AC are equal, BD must be equal to DC. Therefore, BD = DC = 4 cm. Now we can use Pythagoras’ Theorem to calculate height AD : Therefore (b) 11.3 Area of quadrilaterals A plane figure bounded by four straight lines is called a quadrilateral. The calculation of area of some of the quadrilaterals is explained in this section. Example 11.2 Find the area of the shapes shown in Figure 11.2. Figure 11.2 Solution: (a) Area of a rectangle = length × width Length = 15 cm, and width = 6 cm Area of rectangle ABCD = 15 × 6 = 90 cm 2 (b) In a square, the length is equal to the width...
- Fuchang Liu(Author)
- 2017(Publication Date)
- Routledge(Publisher)
...In a rectangle where the two pairs of sides are different in their linear distances (I’ve intentionally avoided using length here), length is one dimension and width is the other. It really doesn’t matter one way or the other. It doesn’t make any difference either. For example, suppose the longer side of a rectangle is 8 centimeters and the shorter side is 5 centimeters. If we name the longer side “length” (l = 8) and the shorter side “width” (w = 5), then the perimeter of this rectangle is p = 2 l + 2 w = 2 × 8 + 2 × 5 = 16 + 10 = 26 cm, and its area is a = lw = 8 × 5 = 40 cm 2. Alternatively, if we name the shorter side length (l = 5) and the longer side width (w = 8), then the perimeter is p = 2 l + 2 w = 2 × 5 + 2 × 8 = 10 + 16 = 26 cm, and its area is a = lw = 5 × 8 = 40 cm 2. Not a thing has come up differently. Figure 10.1 A 5 × 5 Square The perimeter and area of a square can be calculated using the formulas for a rectangle because it is a rectangle. A look at this problem in a different perspective will tell us why it shouldn’t matter one way or the other. Suppose there were such a stipulation that the longer sides were called “lengths” and the shorter sides “widths.” How could we accommodate a square? We know a square is a special rectangle and—while it has its own perimeter and area formulas for easier calculation purposes (p = 4 s and a = s 2, where s refers to the side)—any formula for a rectangle should apply to a square as well. For example, if a square has a side of 5 cm (see Figure 10.1), then its perimeter and area are p = 4 s = 4 × 5 = 20 cm and a = s 2 = 5 2 = 25 cm 2. Then, by way of formulas for a rectangle, p = 2 l + 2 w = 2 × 5 + 2 × 5 = 10 + 10 = 20 cm and a = lw = 5 × 5 = 25 cm 2 (in any square, l = w = s), respectively. This should hardly come as a surprise, because if formulas for rectangles didn’t apply to squares, then squares would no longer be rectangles...
