For a piece of land as shown in the figure, ad = 12M, CD = 9m, ∠ ADC = 90 °, ab = 39m, BC = 36m, calculate the area of this land

For a piece of land as shown in the figure, ad = 12M, CD = 9m, ∠ ADC = 90 °, ab = 39m, BC = 36m, calculate the area of this land

If AC is connected, ac2 = Cd2 + ad2 = 122 + 92 = 225,  AC = 15 in RT △ ADC, AB2 = 1521, ac2 + BC2 = 152 + 362 = 1521, ｜ AB2 = ac2 + BC2, ｜ ACB = 90 °, s △ abc-s △ ACD = 12ac · bc-12ad · CD = 12 × 15 × 36-12 × 12 × 9 = 270-54 = 216 in △ ABC

For a piece of land shown in the figure, the angle ADC is equal to 90 degrees. Ad = 12M, CD = 9m, ab = 39m, BC = 36m, calculate the area of this land

Triangle ADC is a right triangle with AC as the hypotenuse, AC = √ (AD & # 178; + CD & # 178;) = 15 in triangle ABC, AC & # 178; + BC & # 178; = 225 + 1296 = 1521 = AB & # 178; so triangle ABC is a right triangle with ab as the hypotenuse, the area of this land = s triangle ADC + s triangle ABC = 1 / 2 × 12 × 9 + 1

As shown in the figure, in the quadrilateral ABCD, ad = BC, ∠ DAB = 50 ° and ∠ CBA = 70 °, P, m and N are the midpoint of AB, AC and BD respectively. If BC = 8, then the perimeter of △ PMN is______ ．

∵ P and N are the middle points of AB and BD, PN = 12ad = 12 × 8 = 4, PN ∥ ad, ∥ NPB = ∥ DAB = 50 °, similarly, PM = 4, ∥ MPa = ∥ CBA = 70 °, ∥ PM = PN = 4, ∥ MPN = 120 ° - 50 ° - 70 ° = 60 °, ∥ PMN is an equilateral triangle, ∥ Mn = PM = PN = 4, ∥ PMN's perimeter is 12