首页
外语
计算机
考研
公务员
职业资格
财经
工程
司法
医学
专升本
自考
实用职业技能
登录
外语
What is the area of the shaded figure?
What is the area of the shaded figure?
admin
2011-01-18
70
问题
What is the area of the shaded figure?
选项
A、
B、
C、
D、
E、
答案
A
解析
This figure may look intimidating, but it’s actually quite harmless. To tackle it, you must first recognize that it can be split into two smaller triangles, as shown in the diagram. Once you’ve separated the triangles, you can start labeling the lengths. The lower triangle has two 45° angles, so it is clearly a right isosceles triangle. That means that we should be able to find the area quickly. An intermediate step will be calculating the lengths of the (equal) sides, which we’ll designate as x. That will also have a follow-on purpose. We’ll be able to use the length x with the full length of the left side of the figure to calculate the length of the rising side of the smaller triangle. First, though, we’ll get back to the lower triangle and the Pythagorean Theorem:
Now we can use the result for x to find that smaller length:
The triangle may not look familiar yet, but the angle at the right is a giveaway. Since it’s a 120° angle, the supplementary angle θ must be 60°. This is because interior and exterior angles along the same line segment must always sum to 180°. Since another angle in the triangle is right (90°), we now can assert that angle σ measures 30°, since all the angles inside a triangle must sum to 180° as well. This means that we have a 30°-60°-90° triangle. One needs to be careful at this point, as it is easy to misidentify the lengths in one of these. Remember, it is not that the lengths are always 1,
, and 2; but that they are always in the ratio of 1:
:2. If the long nonhypotenuse side has a length of one-half
of , then the other sides should be halved as well. The short side will have length 1/2, and the hypotenuse will have length 1.
At this point, as shown in the last diagram, we can ignore all our calculations but those for a few lengths. The area of the original figure is found with just the four numbers in black:
or answer choice A. That’s about it. There are other ways of finding the area, but if you can handle the steps here, you should have little trouble with GMAT geometry.
转载请注明原文地址:https://kaotiyun.com/show/vJtO777K
本试题收录于:
GMAT QUANTITATIVE题库GMAT分类
0
GMAT QUANTITATIVE
GMAT
相关试题推荐
Gestures,abodylanguageofhumanbeings,______widelyfromculturetoculture.
Howthesebigstonesweremovedtothemountaintopsremainsa______,thatis,nobodyknowshow.
SpeakerA:Goodmorning,sir.CanIhelpyou?SpeakerB:Yes,I’mleavingtoday.CanIhavemybillsettled?SpeakerA:Ofcour
Everydirectorneedsanassistantthathecan______totakecareofproblemsthatmayoccurinhisabsence.
Thetrainwill______fromPlatform2at3:45onTuesdaymorning.
Theopeningbetweentherockswasverynarrow,buttheboysmanagedto()through.
In1947agroupoffamouspeoplefromtheartworldheadedbyanAustrianconductordecidedtoholdaninternationalfestivalof
TheannualcampaigntomakeSingapore’sthreemillionpeoplemorepoliteendedyesterdayandwasimmediatelyfollowedbyanother
Onhearingofthecase,ConanDoylewas______thatthemanwasinnocentandimmediatelywenttoworktoascertainthetruthforh
Allthefollowingcasesareon-the-jobsmokingexceptthat______.Inthesecondpartofthepassage,theauthorsuggestsbannin
随机试题
新设分立
对于获得性免疫缺陷综合征,下列哪项不正确
关于留置权的特征和成立条件,下列说法正确的有()。
(2016年)甲将其位于住宅楼顶楼的一套房屋出租给乙,租赁期限2年,月租金9000元,双方对租金支付方式未约定。乙于租赁开始支付了一年租金。租赁第2个月,房屋天花板出现严重漏雨,乙要求甲进行维修,甲以合同并未约定维修条款为由拒绝。因房屋漏水严重影
第三代喹诺酮类药物的抗菌机制是其抑制了细胞的()。
知识就其实质来说,是人脑对客观事物的特征与联系的反映,是客观事物的_______。
影响推理的因素有()。(2018年)
下列技术动作需要采取胸式呼吸的是()
下列叙述中正确的是()。
Theautomobilehasmanyadvantages.Aboveall,itofferspeoplefreedomtogowhereverandwhenevertheywanttogo.Thebasicp
最新回复
(
0
)