26/03/2020 Geometry(Study by Topics Senior Class) 26/03/2020 0Comments by Gate Academy Welcome to your Geometry(Senior Class Maths Study by Topics) NAME EMAIL PHONE NUMBER 1. Each side of the square pyramid shown below measures 10 inches. The slant height, H, of this pyramid measures 12 inches.What is the area, in square inches, of the base of the pyramid? 100 sq. inches 220 sq. inches 200 sq. inches 120 sq. inches 2. In the diagram, ABCD is a rectangle with AE = EF = FB. What is the ratio of the areas of <span id="MathJax-Element-14-Frame" class="mjx-chtml MathJax_CHTML" style="line-height: 0;text-indent: 0px;text-align: left;text-transform: none;font-style: normal;font-weight: 400;font-size: 18.72px;letter-spacing: normal;float: none;direction: ltr;max-width: none;max-height: none;min-width: 0px;min-height: 0px;border: 0px;margin: 0px;padding: 1px 0px;color: #4c4c4c;font-family: 'Open Sans', sans-serif;background-color: #ffffff" role="presentation" data-mathml="ΔCEF">ΔCEF to that of the rectangle? 1/9 1/6 1/2 1/8 3. Two identical circles intersect so that their centers, and the points at which they intersect, form a square of side 1 cm. The area in sq. cm of the portion that is common to the two circles is π/4 -1 π/5 π/4 π 4. Four points A, B, C and D lie on a straight line in the X-Y plane, such that AB = BC = CD, and the length of AB is 1 metre. An ant at A wants to reach a sugar particle at D. But there are insect repellents kept at points B and C. the ant would not go within one metre of any insect repellent. The minimum distance in metres the ant must traverse to reach the sugar particle is 5 1+π 3√2 4π/3 5. A piece of paper is in the shape of a right-angled triangle and is cut along a line that is parallel to the hypotenuse, leaving a smaller triangle. There was 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 square inches before the cut, what is the area (in square inches) of the smaller triangle? 15.465 14.365 16.665 16.565 6. The size of each interior angle of a regular polygon with n sides is 160°. The value of n is 18 14 12 16 7. A point K moves on one side of a straight line /LM/ such that <LKM = 90°. The locus of K is an arc of a circle semi circle a right angled triangle circle 8. An equilateral triangle BPC is drawn inside a square ABCD. What is the value of the angle APD in degrees? 135 90 150 75 9. A vertical tower OP stands at the center O of a square ABCD. Let h and b denote the length OP and AB respectively. Suppose ∠APB = 60° then the relationship between h and b can be expressed as x 3h²=2b² 2h²=b² 2b²=h² 3b²=2h² 10. Each interior angle of an eight sided polygon is equal to 140 degrees 130 degrees 135 degrees 120 degrees 11. All the vertices of an isosceles triangle lie on a circle and each of the base angles of the triangle is 65°. The angle subtended at the centre of the circle by the base of the triangle is 100 degrees 115 degrees 65 degrees 130 degrees 12. In the figure (not drawn to scale) given below, if AD = CD = BC and ∠BCE =96^{0} , how much is the value of ∠DBC? 32° 84° 64° 28° 13. The rectangle below is made up of 12 congruent (same size) squares. Find the perimeter of the rectangle if the area of the rectangle is equal to 432 square cm. 84 cm 25 cm 93 cm 56 cm 14. Which two angles are not supplementary? 89 degrees and 91 degrees 5 degrees and 175 degrees 30 degrees and 150 degrees 23 degrees and 177 degrees 15. A city has two perfectly circular and concentric ring roads, the outer ring road (OR) being twice as long as the inner ring road (IR). There are also four (straight line) chord roads from E1, the east end point of OR to N2, the north end point of IR; from N1, the north end point of OR to W2, the west end point of IR; from W1, the west end point of OR, to S2, the south end point of IR; and from S1 the south end point of OR to E2, the east end point of IR. Traffic moves at a constant speed of 30π km/hr on the OR road, 20π km/hr on the IR road, and 15 5 km/hr on all the chord roads. Amit wants to reach N2 from S1. It would take him 90 minutes if he goes on minor arc S1 – E1 on OR, and then on the chord road E1 – N2. What is the radius of the outer ring road in kms? 60 40 30 20 16. Two circles, both of radii 1 cm, intersect such that the circumference of each one passes through the centre of the other. What is the area (in sq. cm.) of the intersecting region? 4π/3 - √3/4 π/3 - √3/4 2π/3 - √3/2 π/3 - 2/3 17. Euclid has a triangle in mind. Its longest side has length 20 and another of its sides has length 10.Its area is 80. What is the exact length of its third side √290 √270 √250 √260 18. What is the number of distinct triangles with integral valued sides and perimeter 14? 3 4 5 6 19. In the figure below triangle OAB has an area of 72 and triangle ODC has an area of 288. Find x and y, respectively. 12, 34 23, 43 9, 43 20, 14 20. The length of the common chord of two circles of radii 15 cm and 20 cm, whose centres are 25 cm apart, is 20 cm 15 cm 25 cm 24 cm 21. Consider two different cloth-cutting processes. In the first one, n circular cloth pieces are cut from square cloth piece of side a in the following steps: the original square of side a is divided into nsmaller squares, not necessarily of the same size, then a circle of maximum possible area is cut from each of the smaller squares. In the second process, only one circle of maximum possible area is cut from the square of side a and the process ends there. The cloth pieces remaining after cutting the circles are scrapped in both the processes. The ratio of the total area of scrap cloth generated in the former to that in the latter is √2:1 1:1 n(4-π)/ 4n-π 4n-π/ (4-π) 22. There are two concentric circles such that the area of the outer circle is four times the area of the inner circle. Let A, B and C be three distinct points on the perimeter of the outer circle such that AB and AC are tangents to the inner circle. If the area of the outer circle is 12 square centimeters then the area (in square centimeters) of the triangle ABC would be 9/π 9√3/π π12 6√3/π 23. A ladder leans against a vertical wall. The top of the ladder is 8 m above the ground. When the bottom of the ladder is moved 2 m farther away from the wall, the top of the ladder rests against the foot of the wall. What is the length of the ladder? 10 m 15 m 17 m 20 m 24. Each side of the square pyramid shown below measures 10 inches. The slant height, H, of this pyramid measures 12 inches.What is h, the height, in inches, of the pyramid? 45 inches √59 inches √119 inches √35 inches 25. Ten straight lines, no two of which are parallel and no three of which pass through any common point, are drawn on a plane. The total number of regions (including finite and infinite regions) into which the plane would be divided by the lines is 255 2014 1024 56 1 out of 25 Time is Up! Time's up