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# In the figure above, if PQ is parallel to OR, what is the area of quad

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Math Expert
Joined: 02 Sep 2009
Posts: 43381
In the figure above, if PQ is parallel to OR, what is the area of quad [#permalink]

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11 Dec 2017, 22:04
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25% (medium)

Question Stats:

90% (01:35) correct 10% (01:00) wrong based on 20 sessions

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In the figure above, if PQ is parallel to OR, what is the area of quadrilateral PQRO?

(A) 9
(B) 14
(C) 18
(D) 36
(E) cannot be determined

[Reveal] Spoiler:
Attachment:

2017-12-12_1001.png [ 7.97 KiB | Viewed 301 times ]
[Reveal] Spoiler: OA

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Joined: 31 Jul 2017
Posts: 166
Location: Malaysia
WE: Consulting (Energy and Utilities)
Re: In the figure above, if PQ is parallel to OR, what is the area of quad [#permalink]

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11 Dec 2017, 22:14
Bunuel wrote:

In the figure above, if PQ is parallel to OR, what is the area of quadrilateral PQRO?

(A) 9
(B) 14
(C) 18
(D) 36
(E) cannot be determined

[Reveal] Spoiler:
Attachment:
2017-12-12_1001.png

Area should be 4*4 + 0.5*4*1 = 18
VP
Joined: 22 May 2016
Posts: 1260
In the figure above, if PQ is parallel to OR, what is the area of quad [#permalink]

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13 Dec 2017, 19:45
Bunuel wrote:

In the figure above, if PQ is parallel to OR, what is the area of quadrilateral PQRO?

(A) 9
(B) 14
(C) 18
(D) 36
(E) cannot be determined

[Reveal] Spoiler:
Attachment:
2017-12-12_1001.png

We have a trapezoid with height OP and bases OR and PQ

Length of PQ
∆ OPQ is right isosceles with equal sides OP and PQ

--The angle at P is 90°

PQ || OR. The two segments are cut by traversal OP. Same-side interior angles sum to 180.
∠ POR = 90, hence the angle at P is also 90

-- ∠ PQO = 45. Parallel lines are cut by the traversal OQ, and ∠ QOR = 45. As an alternate interior angle, ∠ PQO also = 45°

-- ∠ POQ is 45: the right angle at vertex O has one angle marked as 45°; 90 - 45 = 45 = ∠ POQ

--OP = PQ: sides opposite equal angles of a triangle are equal

--OP = 4 = PQ, which is one base of the trapezoid

Height, other base, and area

The height of the trapezoid is OP = 4 (Height is perpendicular to base; OP is perpendicular to OR and PQ.)

The other base is OR = 5

Area of trapezoid: $$\frac{(base_1 + base_2)}{2} * h$$

$$(\frac{4 + 5}{2}) * 4 = (4.5 * 4)= 18$$

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In the figure above, if PQ is parallel to OR, what is the area of quad   [#permalink] 13 Dec 2017, 19:45
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