Tag: maths

Quizzes (518) Questions (9324)

Questions Related to maths

Multiple choice maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

Given that a right angled trapezium has an inscribed circle. then " the length of the right angled leg is the Harmonic mean of the lengths of bases. "that  statement is __

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a right-angled trapezium with an inscribed circle, the height (the right-angled leg) is indeed the geometric mean of the bases, and the harmonic mean relationship is a known property.

Multiple choice maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

If $ABCD$ is a trapezium such that $AB\parallel CD$. Also $CD\bot BC$. If $\angle ADB=\theta, BC=p, CD=q$ then $AB$=?

  1. $(p^{2}+q^{2})\cos\theta/p\cos\theta+q\sin\theta$
  2. $(p^{2}+q^{2})\cos\theta/p\sin\theta+q\cos\theta$
  3. $(p^{2}+q^{2})\sin\theta/p\cos\theta+q\sin\theta$
  4. $(p^{2}+q^{2})\sin\theta/p\sin\theta+q\cos\theta$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the properties of a right-angled trapezium where CD is perpendicular to BC, we can use trigonometry in the triangles formed by the diagonals. By expressing the lengths in terms of theta, p, and q, the derived expression matches option A.

Multiple choice maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

$ABCD$ is a trapezium in which $AB\parallel CD$. Which of the following is equal to $AC^{2}+BD{2}$?

  1. $AD^{2}+BC^{2}-2AB.CD$
  2. $AD^{2}+BC^{2}+2AB.CD$
  3. $AD^{2}-BC^{2}+2AB.CD$
  4. $AD^{2}-BC^{2}-2AB.CD$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For any trapezium ABCD with AB parallel to CD, the sum of the squares of the diagonals AC and BD is given by the relation AC^2 + BD^2 = AD^2 + BC^2 + 2(AB)(CD). This can be derived using vector methods or the law of cosines on the triangles formed by the diagonals and sides.

Multiple choice maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

In trapezium PQRS, PQ($23$cm) and RS($13$ cm) are the bases. Find the area of the trapezium if the diagonals bisect angles SPQ and PQR.

  1. $350$ $cm^2$
  2. $276$ $cm^2$
  3. $216$ $cm^2$
  4. $410$ $cm^2$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If the diagonals bisect the base angles of a trapezium, the non-parallel sides are equal to the segments of the base. With bases 23 and 13, the non-parallel sides are 13 each. The height can be calculated using the Pythagorean theorem, and then the area is found.

Multiple choice maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

$ABCD$ is a trapezium in which $BC \parallel AD, BC=20\ cm$ and $AD=45\ cm$. If $P$ and $Q$ are the midpoints of $AB$ and $CD$ respectively, then the ratio of $ar(\Box PBCQ)$ to $ar(\triangle PQD)$ is

  1. $\dfrac{42}{13}$
  2. $\dfrac{13}{6}$
  3. $\dfrac{21}{13}$
  4. $\dfrac{13}{7}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given the midpoints P and Q, the area of the resulting shapes can be calculated using the properties of trapeziums and triangles. The ratio of the areas is derived from the geometric properties of the segments.

Multiple choice maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

The area of a trapezium is  $385 { cm } ^ { 2 } .$  Its parallel sides are in the ratio  $3 : 4$  and the perpendicular distance between them is  $11 { cm } .$  Its longer side is

  1. $35 cm$
  2. $30 cm$
  3. $40 cm$
  4. $60 cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the parallel sides be 3x and 4x. The area of a trapezium is given by (1/2) * (sum of parallel sides) * height. Thus, 385 = (1/2) * (3x + 4x) * 11. Solving this yields 385 = (7x / 2) * 11, so 385 = 38.5x, which means x = 10. The longer side is 4x = 4 * 10 = 40 cm.

Multiple choice maths when lines join trapeziums and kites quadrilaterals and their properties closed figures

In a trapezium, the lengths of its parallel sides are $a$ and $b$. The length of the line joining the midpoints of its non-parallel sides is :

  1. $\dfrac{a-b}{2}$
  2. $\dfrac{a+b}{2}$
  3. $\dfrac{ab}{2}$
  4. $\dfrac{ab}{a+b}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The line segment joining the midpoints of the non-parallel sides of a trapezium is known as its median. The length of this line segment is always equal to half the sum of the lengths of the parallel sides, expressed as (a + b) / 2.