1. Find the cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of ₹ 3 per m². 2. Find the area of the isosceles triangle whose perimeter is 11 cm and the base is 5 cm. 3. Find the area of the equilateral triangle whose each side is 8 cm. 4. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.

1. Find the cost of levelling the ground in the form of a triangle having the sides 51 m, 37 m and 20 m at the rate of ₹ 3 per m².

a = 51 m, b = 37 m, c = 20 m

semiperimeter:  p = (51+37+20):2 = 54 m

Area of triangle:

Rate:  ₹ 3 per m².

Cost:  ₹ 3•306 = ₹ 918

2. Find the area of the isosceles triangle whose perimeter is 11 cm and the base is 5 cm.

a = 5 cm

a+2b = 11 cm  ⇒  2b = 6 cm   ⇒  b = 3 cm

p = 11:2 = 5.5

3. Find the area of the equilateral triangle whose each side is 8 cm.

a = b = c = 8 cm

p = (8•3):2 = 12 cm

4. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.

a = 2x

b = 3x

2x + 2•3x = 32 cm  ⇒ 8x = 32 cm   ⇒  x = 4 cm  ⇒ a = 8 cm, b = 12 cm

p = 32:2 = 16 cm

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.