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In the figure given below, AB || DC || EF, AD || BC and ED || FA. Prove that: Area of DEFH = Area of ABCD
no 12 a) Q12.(a) In the figure (1) given below, ABCD and AEFG are two parallelograms. Prove that area of || gm ABCD = area of || gm AEFG.
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Syllabus
the length of BD.
b. In figure.ii.given below, angle PSR=90?,PQ=10cm,QS=6cm and R Q=9cm. Calculate the length of PR.
c. In figure.iii. given below, angle D=90?,AB=16cm,BC=12cm and CA=6cm .Find CD.
10. In the figure given alongside, squares ABDE and AFGC are drawn on the side AB and the hypotenuse AC of the right triangle ABC.
IF BH is perpendicular is FG, prove that :
(ii) Area of the square ABDE = Area of the rectangle ARHF.
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ANS: 192cm2.
9. In the given figure, AP is parallel to BC, BP is parallel to CQ. Prove that the areas of triangles ABC and BQP are equal.
(i)BG if AD = 6 cm.
(ii)CF if GE =2.3 cm.
(iii)AB if BC = 2.4 cm.
(iv)ED if FD = 4.4 cm.
Q.6. In the figure given below, ABC is an equilateral triangle in which P and S are the mid-points of arcs AB and AC respectively. Prove that: PQ = QR = RS.
In the figure given below, AB || DC || EF, AD || BC and ED || FA. Prove that: Area of DEFH = Area of ABCD
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answer;1000 metre cube.
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Ans:32cm2
no 12 a)
Q12.(a) In the figure (1) given below, ABCD and AEFG are two parallelograms. Prove that area of || gm ABCD = area of || gm AEFG.
Area of traingle (ADC = AEB)
Area of traingle (BOD = COE)
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6. (i) Draw a rectangle ABCD with base 4 cm and diagonal BD = 5 cm. Measure CB. Take any point P on AD. Join BP. From C draw a line parallel to BP to meet AP produced at Q.
(ii) What type of quadrilateral is PBCQ ?
(iii) Prove that the area of the rectangle ABCD is equal to that of the figure PBCQ.
(iv) Prove that the area of the triangle PBC is half the area of the rectangle ABCD.
i) Area of triangle AGB = 2/3 * Area of triangle ADB
ii) Area of triangle ABG = 1/3 * Area of triangle ABC
Show that:
(i) Area (?ADC) = Area (?AEB)
(ii) Area (?BOD) = Area (?COE).
10. ABC is a triangle in which AB=AC=4 cm and . Calculate the area of ABC. Also find the length of perpendicular from A and BC.
Hint: By Pythagoras theorem, BC2=AB2+AC2=42+42=32 BC =4cm.
Q.15. If the perimeter of a right angled triangle is 60 cm and its hypotenuse is 25 cm, find its area.
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Answer: 8 units,40sq.units.
Q.5. The base of a right angled triangle is 12 cm and its hypotenuse is 13 cm long. Find its area and the perimeter.
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Q.9 (i) If the lengths of the sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 48 cm, find its area.
Q. ABCD is a rectangle and P is the midpoint of AB. DP is produced to meet CB at Q prove that area of rectangle ABCD equal to area of triangle DQC.
from chapter theorems on area
Pls answer fast today is my exam.
Q10. In the given figure, AP is parallel to BC, BP is parallel to CQ. Prove that areas of triangles ABC and BQP are equal.
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Q.14. In ABC, , AB = (2x + 1) cm and BC = (x + 1) cm. If the area of the ABC is 60 , find its perimeter.