In triangle ABC, the sides a, B and C opposite to a, B and C, side C = 7 / 2, and Tana + tanb = root 3 × Tanatan B - radical 3, and triangle ABC In triangle ABC, the sides a, B and C opposite to a, B and C, side C = 7 / 2, and Tana + tanb = root 3 × Tanatanb - root sign 3, and the area of triangle ABC is (3 times root sign 3) / 2. Find the value of a + B

In triangle ABC, the sides a, B and C opposite to a, B and C, side C = 7 / 2, and Tana + tanb = root 3 × Tanatan B - radical 3, and triangle ABC In triangle ABC, the sides a, B and C opposite to a, B and C, side C = 7 / 2, and Tana + tanb = root 3 × Tanatanb - root sign 3, and the area of triangle ABC is (3 times root sign 3) / 2. Find the value of a + B

Tan (a + b) = negative radical 3, a + B = 120 °, C = 60 °. S = 1 / 2 absinc, so AB = 6. Cosine theorem C = a + B - 2abcosc, bring in the known value to a + B, and + 2Ab get (a + b) square = 121 / 4, so the answer is 11 / 2

A trapezoidal land area is 16 square meters, the upper bottom is 4.6 meters, the height is 3.2 meters, and how many meters is the lower bottom?

Set the bottom of the trapezoid as X meters,
（4.6+x） × 3.2÷2=16，
       14.72+3.2x=32，
             3.2x=17.28，
                x=5.4；
A: the bottom is 5.4 meters

The area of a trapezoidal land is 16 square meters, the upper bottom is 4.6, the height is 3.2, and how many meters is the lower bottom

(4.6+x) × 3.2÷2=16
x=5.4

A trapezoidal land area is 16 square meters, the upper bottom is 4.6 meters, the height is 3.2 meters, and how many meters is the lower bottom?

Because the area of the trapezoid is equal to [top bottom plus bottom] × High divided by 2
So the trapezoidal area multiplied by 2 divided by the height minus the upper bottom is the lower bottom
The specific steps are as follows;
sixteen × 2÷3.2－4.6＝5.4

Use two identical trapezoids to form a parallelogram. It is known that the area of each trapezoid is 24 square decimeters. What is the area of the parallelogram?

twenty-four × 2 = 48 square decimeters
Answer: the area of the parallelogram is 48 square decimeters

As shown in the figure, in △ ABC, D is a point on BC. If AB = 10, BD = 6, ad = 8, AC = 17, calculate the area of △ ABC

∵BD2+AD2=62+82=102=AB2，
△ abd is a right triangle,
∴AD⊥BC，
In RT △ ACD, CD =
AC2−AD2＝
172−82＝15，
∴S△ABC=1
2BC•AD＝1
2(BD+CD)•AD＝1
two × twenty-one × 8＝84，
Therefore, the area of △ ABC is 84
Answer: the area of △ ABC is 84