The diagram shows a parallelogram, with one side produced. Use the data on the diagram to find the value of $x$, $y$, and $z$. Give a reason for your answer in each case. The area of the parallelogram $ABCD$ is 480 $m^2$. (i) Find the area of the triangle $ABD$. (ii) $E$ is the midpoint of $[CD]$. Find the area of the triangle $BCE$.

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The diagram shows a parallelogram, with one side produced - Leaving Cert Mathematics - Question 4 - 2015

Question 4

The diagram shows a parallelogram, with one side produced. Use the data on the diagram to find the value of $x$, $y$, and $z$. Give a reason for your answer in each... show full transcript

Worked Solution & Example Answer:The diagram shows a parallelogram, with one side produced - Leaving Cert Mathematics - Question 4 - 2015

Step 1

$x = $

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114 rated

Answer

30°

Reason: Alternate angles

Step 2

$y = $

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Answer

40°

Reason: Angle sum in a triangle is 180°.

Step 3

$z = $

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Answer

70°

Reason: Corresponding angles/ External angle equals sum of opposite interior angles.

Step 4

Find the area of the triangle $ABD$.

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Answer

|\Delta ABD| = \frac{1}{2} \times 480 = 240 m^2

Step 5

Find the area of the triangle $BCE$.

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Answer

|\Delta BCE| = \frac{1}{2} |\Delta ABCD| = \frac{1}{2} \times 480 = 120 m^2

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