See diagram.

Take AB as the base of the parallelogram.

Then draw perpendiculars from P and R on to AB. Since AB || CD, the two perpendiculars are parallel and equal to the altitude of the parallelogram with AB as the base.

The area of triangle PAB = area of RAB = 1/2 * AB * altitude.

Area of parallelogram ABCD = AB * altitude = twice that of the triangles.

= 16 cmsquare.

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see diagram.

Take a circle of radius R. Two congruent circles mean that their radii are same. So we can work with one circle itself. So I draw two chords AB and DE of equal length L. C is the center of circle.

Look at the triangles CAB and CDE. The sides AB = DE, given. Then CA = CB = CD = CE = radius of the triangle. Hence the two triangles are congruent. Hence angles ACB and angle DCE are same. So the angles subtended are same.

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3.

Draw a line horizontally in the middle of paper sheet, and measure 5 cm using a ruler. Mark the end points as A and B. Now using the perpendicular bisector method using compass or by using protractor draw a line AD at A and a line BC at B , both perpendicular to the line AB. Use the ruler or the compass measuring 5 cm, to cut off these BC and AD at 5 cm. Now join CD.

you have the square.

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4 In parallelogram ABCD, the diagonal BD bisects angle B. Means that

angle ABD = angle DBC.

AD || BC. and BD is a transversal line cutting the two parallel lines.

Hence, we have angle ADB = angle DBC as they are alternate angles.

also angle ABD = angle BDC as they are alternate angles.

Since angle ABD = angle DBC, the other two angles ADB = angle BDC.

So BD bisects angle D also.

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5

cube edge length = 4 cm

its total surface are a = 6 * 4² = 96 cm²

volume of the cube = 4³ = 64 cm³

volume of small cubes = 1³ cm³

number of small cubes made from the big cube : 64 cm³/1 cm³ = 64

surface area of all 64 small cubes : 64 * 6 * 1² = 384 cm²

increase in surface area = 384 - 96 = 288 cm²

*% increase = 288/96 * 100 = 300%*