![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
In △ ABC, it is known that BD and CE are the midlines on both sides respectively, and BD ⊥ CE, BD = 4, CE = 6, then the area of △ ABC is equal to () A. 12 B. 14 C. 16 D. 18
Connect the ED as shown in the figure,
Then s quadrilateral BCDE = 1
2DB•EH+1
2BD•CH=1
2DB（EH+CH）=1
2BD•CE=12．
And ∵ CE is △ ABC center line,
∴S△ACE=S△BCE，
∵ D is the midpoint of AC,
∴S△ADE=S△EDC，
∴S△ABC=4
3S quadrilateral BCDE = 4
three × 12=16．
Therefore, C
In △ ABC, it is known that BD and CE are the midlines on both sides respectively, and BD ⊥ CE, BD = 4, CE = 6, then the area of △ ABC is equal to () A. 12 B. 14 C. 16 D. 18
Connect the ED as shown in the figure,
Then s quadrilateral BCDE = 1
2DB•EH+1
2BD•CH=1
2DB（EH+CH）=1
2BD•CE=12．
And ∵ CE is △ ABC center line,
∴S△ACE=S△BCE，
∵ D is the midpoint of AC,
∴S△ADE=S△EDC，
∴S△ABC=4
3S quadrilateral BCDE = 4
three × 12=16．
Therefore, C
Trapezoidal and triangular area formula analysis diagram
I only know the formula
However, here you are, you know, let me be the best
Divide the trapezoid in the grid into three triangles so that their area ratio is 1:2:3
According to the stem analysis, the following delimitation methods can be obtained:
The height of a triangle and a trapezoid is equal. The bottom of the triangle is 24 cm long, the upper bottom of the trapezoid is 9 cm long, and the lower bottom is 15 cm long. Who's the area of the two figures I only asked when I saw who had a large area! What do you say when you arrive? The same big as that?
Set the height to h,
Then triangle area = 24xhx1 / 2 = 12h
Trapezoidal area = (9 + 15) xhx1 / 2 = 12h,
Therefore, the area of the two figures is equal
The two diagonals of trapezoidal ABCD intersect at point E. there are several pairs of triangles with equal area in the figure
3 pairs. Because triangle ABC and triangle DBC have the same base and equal height, they are a pair
Triangle ACD and triangle abd have the same base and equal height, and are a pair
Triangle AEB and triangle Dec are obtained by subtracting the area of the same triangle ade from triangle ACD and triangle abd respectively, so they are also a pair
RELATED INFORMATIONS
- 1. Draw four small triangles in the square (as shown in the figure). The area ratio of triangles I and II is 2:1; The areas of triangles III and IV are equal; The sum of the areas of triangles I, II and III is 1 4 square meters; The sum of the areas of triangles II, III and IV is 1 6 square meters; So what is the sum of the four small triangles______ Square meters
- 2. The three sides of a right triangle are 3cm, 4cm and 5cm respectively. The area of this triangle is () square centimeters; The height on the hypotenuse is () cm Such as the title! Urgent~
- 3. The three sides of a right triangle are 3cm, 4cm and 5cm respectively. How many square centimeters is the area of the right triangle?
- 4. Given that the lengths of both sides of the triangle are 5 and 7 respectively, the value range of the center line length x of the third side is () A. 2＜x＜12 B. 5＜x＜7 C. 1＜x＜6 D. Unable to determine
- 5. Given that the lengths of both sides of the triangle are 5 and 7 respectively, the value range of the center line length x of the third side is () A. 2＜x＜12 B. 5＜x＜7 C. 1＜x＜6 D. Unable to determine
- 6. 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
- 7. In triangle ABC, ab = 17, AC = 15, the center line ad on the side of BC = 4, calculate the area of triangle ABC
- 8. The perimeter of a right triangle is 2+ 6. If the length of the center line on the hypotenuse is 1, the area of the triangle is equal to () A. 1 B. 1 two C. 1 four D. 3 four
- 9. The circumference of ABC of a right triangle is 24 cm, and the length ratio of its three sides is 3:4:5. Calculate the area of the shaded part
- 10. The ratio of the length of the three sides of a right triangle is 3:5:4. It is known that the circumference of the right triangle is 36 cm. How many square centimeters is its area?
- 11. The area of a triangle is 48cm2, and the area of the triangle surrounded by its three median lines is
- 12. The slope of the straight line L is known to be 1 6, and forms a triangle with an area of 3 with the two coordinate axes, then the equation of straight line L is __
- 13. The lengths of both sides of the triangle are 8 and 6 respectively. The length of the third side is a real root of the univariate quadratic equation x2-12x + 20 = 0. Find the area of the triangle
- 14. If the area of the triangle enclosed by the straight line y = 2x + m on the two coordinate axes is equal to m, the value of M is
- 15. Given that the perimeter of a right triangle is 30 and the area is 30, find the oblique side length of the triangle
- 16. If the perimeter of a right triangle is 5cm and the center line on the hypotenuse is 1cm, the area of this right triangle is?
- 17. In △ ABC, a = 60 °, C: B = 8:5, the area of the inscribed circle is 12 π, and the radius of the circumscribed circle of △ ABC is calculated
- 18. It is known that in △ ABC, the side opposite the acute angle B = 7, the radius of the circumscribed circle r = 7 times the root number 3 / 3, and the triangle area s = 10 times the root number 3. Find the length of the other two sides of the triangle
- 19. In triangular row ABC, a equals 1, C equals 2, and B equals 60 degrees. What is the area of triangular ABC
- 20. In the acute triangle ABC, the opposite sides of angles a, B and C are a, B and C respectively, and the root number 3B = 2asinb is known to calculate the size of the angle; If a = 6, find the range of B + C