The area of the quadrilateral bounded by the \(Y\) -axis, the line \(x = 5\) , and the lines \(|x-y|-|x-5|=2\), is
- 45
- 55
- 60
- None of Above
The Correct Option is A
Solution and Explanation
To find: Area of quadrilateral \( ABDE \)
Approach: The quadrilateral \( ABDE \) is made up of:
- Rectangle \( ABCD \)
- Triangle \( \triangle CDE \)
So, Area of \( ABDE = \) Area of rectangle \( ABCD \) + Area of triangle \( \triangle CDE \)
Step 1: Area of rectangle \( ABCD \)
Length = \( 7 - 3 = 4 \) units
Breadth = \( 5 \) units
Area = \( \text{Length} \times \text{Breadth} = 4 \times 5 = 20 \) square units
Step 2: Area of triangle \( \triangle CDE \)
Given: Base = \( 10 \) units, Height = \( 5 \) units
Area = \( \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 10 \times 5 = 25 \) square units
Step 3: Total Area of Quadrilateral \( ABDE \)
\( = 20 + 25 = \mathbf{45} \) square units
Final Answer: (A) \( \mathbf{45} \)
Top Questions on Mensuration
- OAB is sector of a circle with centre O and radius 7 cm. If length of arc \( \widehat{AB} = \frac{22}{3} \) cm, then \( \angle AOB \) is equal to
- CBSE Class X - 2025
- Mathematics
- Mensuration
On the day of her examination, Riya sharpened her pencil from both ends as shown below.
The diameter of the cylindrical and conical part of the pencil is 4.2 mm. If the height of each conical part is 2.8 mm and the length of the entire pencil is 105.6 mm, find the total surface area of the pencil.- CBSE Class X - 2025
- Mathematics
- Mensuration
Two identical cones are joined as shown in the figure. If radius of base is 4 cm and slant height of the cone is 6 cm, then height of the solid is
- CBSE Class X - 2025
- Mathematics
- Mensuration
From one face of a solid cube of side 14 cm, the largest possible cone is carved out. Find the volume and surface area of the remaining solid.
Use $\pi = \dfrac{22}{7}, \sqrt{5} = 2.2$- CBSE Class X - 2025
- Mathematics
- Mensuration
The radius of a circle with centre 'P' is 10 cm. If chord AB of the circle subtends a right angle at P, find area of minor sector by using the following activity. (\(\pi = 3.14\))
Activity :
r = 10 cm, \(\theta\) = 90\(^\circ\), \(\pi\) = 3.14.
A(P-AXB) = \(\frac{\theta}{360} \times \boxed{\phantom{\pi r^2}}\) = \(\frac{\boxed{\phantom{90}}}{360} \times 3.14 \times 10^2\) = \(\frac{1}{4} \times \boxed{\phantom{314}}\) <br>
A(P-AXB) = \(\boxed{\phantom{78.5}}\) sq. cm.
Questions Asked in CAT exam
- The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.
Certain codes may, of course, be so widely distributed in a specific language community or culture, and be learned at so early an age, that they appear not to be constructed – the effect of an articulation between sign and referent – but to be ‘naturally’ given. Simple visual signs appear to have achieved a ‘near-universality’ in this sense: though evidence remains that even apparently ‘natural’ visual codes are culture specific. However, this does not mean that no codes have intervened; rather, that the codes have been profoundly naturalized. The operation of naturalized codes reveals not the transparency and ‘naturalness’ of language but the depth, the habituation and the near-universality of the codes in use. They produce apparently ‘natural’ recognitions. This has the (ideological) effect of concealing the practices of coding which are present.- CAT - 2024
- Para Summary
- There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.
Sentence: Taken outside the village of Trang Bang on June 8, 1972, the picture captured the trauma and indiscriminate violence of a conflict that claimed, by some estimates, a million or more civilian lives.
Paragraph: The horrifying photograph of children fleeing a deadly napalm attack has become a defining image not only of the Vietnam War but the 20th century. Dark smoke billowing behind them, the young subjects' faces are painted with a mixture of terror, pain and confusion. (2) Soldiers from the South Vietnamese army's 25th Division follow helplessly behind. (3) The picture was officially titled "The Terror of War," but the photo is better known by the nickname given to naked 9-year-old at its centre "Napalm Girl". (4)- CAT - 2024
- Para Completion
- There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.
Sentence: Understanding central Asia’s role helps developments make more sense not only across Asia but in Europe, the Americas and Africa.
Paragraph: The nations of the Silk Roads are sometimes called ‘developing countries’, but they are actually some of the world’s most highly developed countries, the very crossroads of civilization, in advanced states of disrepair. ___(1)___. These countries lie at the centre of global affairs: they have since the beginning of history. Running across the spine of Asia, they form a web of connections fanning out in every direction, routes along which pilgrims and warriors, nomads and merchants have travelled, goods and produce have been bought and sold, and ideas exchanged, adapted and refined. ___(2)___ .They have carried not only prosperity, but also death and violence, disease and disaster. ___(3)___. The Silk Roads are the world’s central nervous system, connecting otherwise far-flung peoples and places…. ___(4)___. It allows us to see patterns and links, causes and effects that remain invisible if one looks only at Europe, or North America.- CAT - 2024
- Para Completion
- There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.
Sentence: The brain isn’t organized the way you might set up your home office or bathroom medicine cabinet.
Paragraph: ___(1)___. You can’t just put things anywhere you want to. The evolved architecture of the brain is haphazard and disjointed, and incorporates multiple systems, each of which has a mind of its own. ___(2)___. Evolution doesn’t design things and it doesn’t build systems—it settles on systems that, historically, conveyed a survival benefit. There is no overarching, grand planner engineering the systems so that they work harmoniously together. ___(3)___. The brain is more like a big, old house with piecemeal renovations done on every floor, and less like new construction. ___(4)___.- CAT - 2024
- Para Completion
- There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.
Sentence: Yet each day the flock produced eggs with calcareous shells though they apparently had not ingested any calcium from land which was entirely lacking in limestone.
Paragraph: Early in this century a young Breton schoolboy who preparing himself for a scientific career began to notice a strange fact about hens in his father's poultry yard. ___(1) ___. As they scratched the soil they constantly seemed to be pecking at specks of mica, a siliceous material dotting the ground. ___(2)___. No one could explain to Louis Kervran why the chickens selected the mica, or why each time a bird was killed for the family cooking pot no trace of the mica could be found in its gizzard. ___(3) ___. It took Kervran many years to establish that the chickens were transmuting one element into another. ___(4)___.- CAT - 2024
- Para Completion