Question
Construct a quadrilateral ABCD, given that AB = 8cm, BC = 8cm, CD = 10cm, AD = 10cm and $\angle\text{A}=45^\circ.$
✓
Answer
Steps of Construction:Step I: Draw AB = 8cm.
Step II: Construct $\angle\text{BAD}=45^\circ.$
Step III: With A as the centre and radius 10cm, cut off AD = 10cm.
Step IV: With D as the centre and radius 10cm, draw an arc.
Step V: With B as the centre and radius 8cm, draw an arc to intersect the arc drawn in Step IV at C.
Step VI: Join BC and CD to obtained the required quadrilateral.
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Observe the following pattern,
$1^2=\frac{1}{6}\big[1\times(1+1)\times(2\times1+1)\big]$
$1^2+2^2=\frac{1}{6}\big[2\times(2+1)\times(2\times2+1)\big]$
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$1^2+2^2+3^2+4^2=\frac{1}{6}\big[4\times(4+1)\times(2\times4+1)\big]$
and find the values of each of the following:
→$1^2=\frac{1}{6}\big[1\times(1+1)\times(2\times1+1)\big]$
$1^2+2^2=\frac{1}{6}\big[2\times(2+1)\times(2\times2+1)\big]$
$1^2+2^2+3^2=\frac{1}{6}\big[3\times(3+1)\times(2\times3+1)\big]$
$1^2+2^2+3^2+4^2=\frac{1}{6}\big[4\times(4+1)\times(2\times4+1)\big]$
and find the values of each of the following:
- $1^2+2^2+3^2+4^2+\ .....\ +10^2$
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