Tag: closed figures

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

In trapezium $ABCD,\ \overline {AD} \parallel \overline {BC} $ and $\overline {AC} \bigcap  \overline {BD}=\left{P\right}$. If $PD=9,\ PA=5$ and $PB=7.2$ then $AC=........\ .$

  1. $4$
  2. $12$
  3. $13$
  4. $9$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In a trapezium, the diagonals intersect such that triangles ADP and BCP are similar. Using the ratio of segments PA/PC = PD/PB, we find PC = (PA * PB) / PD = (5 * 7.2) / 9 = 4. Then AC = PA + PC = 5 + 4 = 9.

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

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.