Explanation:
remember : 1 m (meter) = 100 cm (centimeter)
and if you don't have then in your books, all the formulas can be easily found on the internet.
(a)
the area of a trapezoid is
height × (baseline + top line) / 2
in our case
14 × (35 + 12.5) / 2 = 14×47.5/2 = 7×47.5 = 332.5 cm²
(b)
the area of a parallelogram is
baseline × height
in our case
1.7 m × 90 cm = 1.7 m × 0.9 m = 1.53 m²
(c)
the same as in (b), just here we have only cm.
the area is
21 cm × 19 cm = 399 cm²
(d)
the area of a triangle is
baseline × height / 2
in case of a right-angled triangle either of the legs are automatically the height towards the other leg.
so, the area is
15 × 20 / 2 = 15 × 10 = 150 cm²
(e)
the same formula as in (d) for general triangles. since we have the baseline and the height, we don't need the other information.
the area is
17 × 7 / 2 = 119 / 2 = 59.5 cm²
(f)
the same formula applies again as in (d), as it really applies to all forms of triangles.
the area is
13 × 11 / 2 = 143/2 = 71.5 cm²
(g)
and again the triangle formula. just note that this time the height goes to the 112 cm side, which makes it the baseline (it does not matter that it is not flat "on the ground", what matters is that the height is going to it in a right angle).
the area is
112 × 41 / 2 = 56 × 41 = 2296 mm²
(h)
this is a quadrilateral, where the diagonals intersect at right angles.
so, we can see it as the combination of 2 triangles with given baselines and heights. either left-right or top-down.
I choose the top-down view.
the baseline of both triangles is the horizontal diagonal (15 + 12 = 27 cm). one height is 8 cm, the other 10 cm.
the area of the top triangle is then
27 × 8 / 2 = 27 × 4 = 108 cm²
the area of the bottom triangle is
27 × 10 / 2 = 27 × 5 = 135 cm²
the area of the whole quadrilateral is then
108 + 135 = 243 cm²
(i)
we cannot calculate the area of that parallelogram. we have to little information.
given the baseline length of 7 cm and the length of one diagonal of 10 cm we can draw infinitely many different parallelograms with different areas. just use the parallelogram as it is drawn and then turn the diagonal up and up until it is almost covering the 7 cm side. all these parallelograms that would be created by this movement have the same 7cm side and 10cm diagonal but different areas.