26/03/2020Geometry(Study by Topics Senior Class) 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 h, the height, in inches, of the pyramid? √35 inches √119 inches √59 inches 45 inches2. What is the number of distinct triangles with integral valued sides and perimeter 14? 4 3 6 53. In the figure given below, ABCD is a rectangle. The area of the isosceles right triangleABE = 7cm^{2}; EC = 3(BE). The area of ABCD (in cm^{2}) is 42 cm² 21 cm² 28 cm² 56 cm²4. In the diagram, ABCD is a rectangle with AE = EF = FB. What is the ratio of the areas of ΔCEF">ΔCEF to that of the rectangle? 1/6 1/2 1/9 1/85. Which of the following statements is false? An equilateral triangle is also equiangular If two triangles are similar, then they are also congruent An equiangular triangle is also equilateral If two triangles are congruent, then they are also similar6. Each interior angle of an eight sided polygon is equal to 130 degrees 140 degrees 135 degrees 120 degrees7. In the following figure, the diameter of the circle is 3 cm. AB and MN are two diameters such that MN is perpendicular to AB. In addition, CG is perpendicular to AB such that AE:EB = 1:2, and DF is perpendicular to MN such that NL:LM = 1:2. The length of DH in cm is (3√2-1)/ 2 (2√2-1)/ 3 (2√2-1)/ 2 2√2-18. 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 120 sq. inches 220 sq. inches 200 sq. inches9. 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 20, 14 23, 43 9, 4310. The figure below shows two concentric circles with centre O. PQRS is a square inscribed in the outer circle. It also circumscribes the inner circle, touching it at points B, C, D and A. What is the ratio of the perimeter of the outer circle to that of polygon ABCD? π/2 π/4 π 3π/211. The chord BA is extended to a point T such that CT becomes a tangent to the circle at pointIf ∠ATC = 30° and ∠ACT = 50°, then the angle ∠BOA is 80° 100° 2° 150°12. In the diagram given below, ∠ABD = ∠CDB = ∠PQD = 90° . If AB:CD = 3:1, the ratio of CD: PQ is 1:0.69 0.5 : 1 1 :0.75 1: 0.7213. The sides /AB/ and /AC/ of a triangle ABC are produced to D and E respectively such that <DBC = 125° and <BCE = 95°. Find the value of <BAC 85 degrees 55 degrees 40 degrees 90 degrees14. Find the size of angle x in the figure below 84° 56° 24° 36°15. 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? 2π/3 - √3/2 4π/3 - √3/4 π/3 - √3/4 π/3 - 2/316. A semi-circle is drawn with AB as its diameter. From C, a point on AB, a line perpendicular to AB is drawn meeting the circumference of the semi-circle at D. Given that AC = 2 cm and CD = 6 cm, the area of the semi-circle (in sq. cm) will be 32π 40.5π 50π 81π17. Find the volume of a closed conical container with radius 5 cm and a height of 15 cm. 393 254 124 48318. A point K moves on one side of a straight line /LM/ such that <LKM = 90°. The locus of K is semi circle circle a right angled triangle an arc of a circle19. Which of the following specified sets of data is not necessarily sufficient for the construction of a triangle? Two sides and an included angle Two sides and a right angle Three sides Three angle20. When two straight lines intersect I. adjacent angles are equal II. adjacent angles are supplementary III. vertically opposite angles are equalIV. vertically opposite angles are supplementary Which of the above statements are true? II and IV only I and IV only II and III only I and III only21. 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 4n-π/ (4-π) 1:1 n(4-π)/ 4n-π22. 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 π π/5 π/4 -123. 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 3√2 4π/3 1+π 524. ABC is a right triangle with the size of angle ACB equal to 74 degrees. The lengths of the sides AM, MQ and QP are all equal. Find the measure of angle QPB. 148° 35° 94° 135°25. In the figure (not drawn to scale) given below, if AD = CD = BC and ∠BCE =96^{0} , how much is the value of ∠DBC? 28° 32° 84° 64°26 out of 25Time is Up!