Area of a Kite
The area of a kite can be calculated using the formula A = (d1 * d2) / 2, where d1 and d2 are the lengths of the diagonals. A kite is a quadrilateral with two distinct pairs of adjacent sides that are equal in length. The area of a kite is half the product of its diagonals.
4 Key excerpts on "Area of a Kite"
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...
- Sandra Rush(Author)
- 2013(Publication Date)
- Research & Education Association(Publisher)
...The area of a trapezoid is given by This formula is the same as the one provided on the GED ® test formula sheet: since multiplication is commutative (xy is the same as yx; see Chapter 2). Parallelogram A parallelogram is a quadrilateral (four-sided figure) with parallel sides, as the name implies. In this case, it is a step up from the trapezoid because the other two sides are also parallel. So a parallelogram has two pairs of parallel sides, and the parallel sides are equal to each other. The perimeter of a parallelogram is still the sum of the lengths of all four sides. So the perimeter of the above parallelogram is JK + KL + LM + MJ. In general, if the lengths of the sides of a parallelogram are, say, q, r, s, and t, its perimeter is Since the sides opposite each other are equal as well as being parallel, if q = r and s = t, then the perimeter can be rewritten as Thus, the perimeter of a parallelogram is twice the sum of the two unequal sides. The area of a parallelogram is given by the general formula of base × height, where the height is perpendicular to the base: The diagonals of a parallelogram bisect each other. 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...
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...
eBook - ePubHands-On Geometry
Constructions With a Straightedge and Compass (Grades 4-6)
- Christopher M. Freeman(Author)
- 2021(Publication Date)
- Routledge(Publisher)
...On the picture in the upper right corner of the page, lightly draw all four sides of kite ACBD; is its main diagonal. Name ___________________________________ Date ______________________________ Lesson 2.5 Construct a Square When Given Its Diagonal A square is a special type of kite that has four equal sides and four equal angles. The four corners of a square lie on a circle. See the example to the right. Using below as a diagonal, construct a square following the directions below. Construct the perpendicular bisector of (Follow the procedure you learned in Lesson 2.4.) Label the midpoint of R. Draw a circle with center R and passing through S. Label the points where the circle crosses the perpendicular bisector, Q and A. Use your straightedge to draw,,, and SQUA is a square! Name ______________________________________ Date ________________________________ Lesson 2.6 Bisect an Angle An angle is made up of two rays with a common endpoint. The rays are called the sides of the angle. The endpoint is called the vertex of the angle. We often use the vertex point to name the angle; for example, the angle in the middle of this page called "angle B." To bisect an angle means to draw a ray that splits the angle into two equal angles. The ray is called an angle bisector. Our angle bisector will be the main diagonal of a kite. Follow the directions below to bisect angle B. Draw an arc with center B and a radius of your choice, but not too small. Label the points where the arc crosses each side of the angle, A and C. Draw an arc with center A. With the same radius, draw an arc with center C. Label the point where the two arcs cross, D. Draw a ray from B through D. This ray bisects angle B. (Imagine drawing and Do you see that BADC would be a kite?) 6...
