As shown in the figure, the side length of the small square in the grid is 1, the three vertices of the triangle ABC, and the three vertices of the triangle ABC are all on the grid points. Find the height on the AB side of the triangle ABC (the figure is a 3 × 3 square, and the three sides of the square are root 2 and 2 root signs 13)

S ⊿ ABC = (2 √ 2 + √ 2 / 2) ×√ 2 / 2 = 5 / 2 = 13 × H / 2 h = 5 / √ 13 [I guess AB = √ 13]

As shown in the figure, in a 4 × 4 square grid, the vertices a, B and C of △ ABC are on the vertex of the unit square. Please draw a △ a1b1c1 in the figure so that △ a1b1c1 ∷ ABC (similarity ratio is not 1), and points A1, B1, C1 are all on the vertex of the unit square______ .

As shown in the figure

In the square grid below, each square vertex is called a grid point. Please draw a square with an area of 13

To draw a square with an area of 13, we should first express the root sign 13. The root sign 13 can be formed in a right triangle, and the hypotenuse of a right triangle with right angles of 2 and 3 is root 13. Four root signs 13 can be used to draw a square with an area of 13
Thank you,

Draw a square in the grid whose area is root 10 Root 10 is not a perimeter

The reasons are as follows:
If the area is root 10, the side length is 4 times and the root number is 10
On a lattice point, AB can be assumed to be an edge, and a to B can be assumed to shift m and then move n vertically to B. thus, the length of AB is under the root sign (m ^ 2 + n ^ 2),
(m ^ 2 + n ^ 2) must be an integer and cannot be the root 10

The side length of each square in the square grid is 1. Take the grid point as the vertex, draw a triangle so that the three sides are root 13, root 34 and root 45 respectively

Just a graduated ruler and compass will do
It's by drawing a right triangle, drawing the hypotenuse, possibly to any length of the side
The basic process is as follows:
1. First draw the edge of length 2, that is √ 4
2. Draw a vertical line of side length 3 along one vertex of side length 2, connect their other two vertices, and get the slope length of √ 13
3. Draw a vertical line with side length 5 along one vertex of side length 3, connect their other two vertices, and get the slope length of √ 34

Using the 4 * 4 grid diagram, make a square with the area of 8 union units, and then draw the positive root 8 and negative root 8 on the number axis

Since it is a 4 * 4 grid, we have already drawn 4 * 4 = 16 unit squares. We only need to connect the middle points of the four sides to get a square of 8 square units. Its side length is the root 8. We only need to take the side length by using a sub rule and draw the points with positive root 8 and negative root 8 at both ends of the origin of the number axis

Draw an isosceles triangle def in a square mesh. Its waist length is root 5, and its vertices are all on the grid. How many triangles can be drawn Attention, not equal to each other

There are five: bottom edges are √ 2, 2, √ 10, 3 √ 2 and 4, as shown in the figure:

The isosceles triangles satisfying the conditions are △ OAB, △ OBC, △ OBD, △ OBE, △ oBf

As shown in the picture is a square grid. The side length of each small square is one centimeter. How many centimeters is the area of the shadow part of the square?

Fifteen

As shown in the figure, given the triangle ABC in the square grid with the side length of 1, try to judge the shape of the triangle

It can be seen from the figure that ab = √ (8? 2 + 1? 2) = √ 65
BC=√(2²+3²)=√13
AC=√(6²+4²)=√52=2√13
Because AB? 2 = BC? 2 + AC? 2 Pythagorean theorem
Therefore, △ ABC is a right triangle with ∠ C as its right angle

As shown in the figure, how many squares are there in a 4x4 grid table?

Let the side length of each small square be 1
There are 42 = 16 squares with side length of 1,
The square with side length 2 has (4-1) 2 = 32 = 9,
The square with side length of 3 has (4-2) 2 = 22 = 4 (pieces),
The square with side length 4 has (4-3) 2 = 12 = 1 (pieces),
There are 16 + 9 + 4 + 1 = 30
A: there are 30 different squares