The geometry exercises provided here cover a wide range of fundamental mathematical concepts, essential for students at different school levels within the English educational system. These exercises are designed to allow students to practice independently using guidelines, course reminders, and methodological advice.
Students in Year 7 and Year 8, for example, can tackle calculations of perimeters and areas of simple geometric figures such as circles, rectangles, and squares. For instance, calculating the perimeter of a circle uses the formula P = 2 × π × r, where r represents the radius of the circle. Similarly, the area of a disk is calculated using the formula A = π × r2, which allows giving an approximate value to two decimal places. Students in Year 9 are introduced to the Pythagorean theorem through exercises such as calculating the hypotenuse of a right triangle using the lengths of the other sides of the triangle.
Students in Year 10 and Year 11 deepen their knowledge in analytic geometry by working on coordinate systems to calculate the coordinates of vectors or the distances between two points. For example, calculating the coordinates of the vector from points A (13, 8) and D (7, 6), or determining the distance between these two points. These exercises are crucial for developing students' skills in analytic geometry. Exercises on vector geometry, such as calculating the coordinates of the midpoint of a segment, are also included to help students understand the basic concepts of vectors in the plane.
Finally, exercises on the perimeters and areas of rectangles and squares allow students in Year 7 and Year 8 to become familiar with basic formulas and practice their application, thus strengthening their skills in geometric calculations. These exercises are essential for preparing students for exams and for developing a solid understanding of basic geometric concepts within the framework of the English school curriculum.
10 exercisesExercise example N°1242 :
The perimeter of a circle is given by the formula `P=2*pi*r`, where r is the radius of the circle.
Give an approximate value to 2 decimal places of the perimeter of a circle of radius 7.
perimeters and areas geometry 6th Grade 7th Grade perimeter_circle
The purpose of this exercise is to calculate the perimeter of a circle knowing its radius.
Exercise example N°1245 :
The area of a disk is given by the formula `A=pi*r^2`, where r is the radius of the circle.
Give an approximate value to 2 decimal places of the area of a disk of radius 14.
perimeters and areas geometry 6th Grade 7th Grade area_circle
The purpose of this corrected exercise is to practice calculating the area of a disk.
Exercise example N°3300 :
In the triangle ABC rectangle in A, we give AB=20 and AC=15..
Calculate BC.
right-angled triangles geometry 8th Grade pythagorean
The purpose of this exercise is to calculate the hypotenuse of a right triangle using the Pythagorean theorem.
Exercise example N°3441 :
Let(O,`vec(i)`,`vec(j)`) be a reference frame of the plane. Let A and D be two points of coordinates `(13,8)` and `(7,6)` respectively in this frame, compute the coordinates of the vector `vec(AD)`.
vectors geometry 9th Grade 10th Grade vector_coordinates
The purpose of this corrected exercise is to calculate the coordinates of a vector from the coordinates of two points.
Exercise example N°3442 :
The plane is given an orthonormal reference frame (O,`vec(i)`,`vec(j)`). Let A and D be two points of coordinates (`13`,`8`) and (`7`,`6`) respectively in this frame, calculate the distance between A and D .
vectors geometry 9th Grade 10th Grade vector_norm
The purpose of this corrected exercise is to calculate the distance between two points from their coordinates.
Exercise example N°3443 :
Let(O,`vec(i)`,`vec(j)`) be a reference frame of the plane. Let D and H be two points of coordinates `(2,8)` and `(2,7)` respectively in this frame, compute the coordinates of the middle of the segment [DH].
vectors geometry 9th Grade 10th Grade
The purpose of this corrected analytical geometry exercise is to calculate the coordinates of the midpoint of a segment from coordinates.
Exercise example N°11201 :
The area of a rectangle is given by the formula L*l where L is the length and l is the width. Calculate the area of a rectangle where L=9 and l=6.
perimeters and areas geometry 6th Grade 7th Grade area_rectangle
The purpose of this corrected exercise is to practice calculating the area of a rectangle.
Exercise example N°11202 :
The area of a square is given by the formula l*l where l is the length of a side. Calculate the area of a square where l=9.
perimeters and areas geometry 6th Grade 7th Grade area_square
The purpose of this corrected exercise is to practice calculating the area of a square.
Exercise example N°11203 :
The perimeter of a rectangle is given by the formula `2*(L+l)`, where L is the length and l the width.
Calculate the perimeter of a rectangle of length L=20 and width l=12.
perimeters and areas geometry 6th Grade 7th Grade perimeter_rectangle
The objective of this exercise is to calculate the perimeter of a rectangle knowing its length and width.
Exercise example N°11204 :
The perimeter of a square is given by the formula 4*l, where l is the length of a side. Calculate the perimeter of a square of length l=20.
perimeters and areas geometry 6th Grade 7th Grade perimeter_square
The objective of this corrected exercise is training in calculating the perimeter of a square knowing the length of a side.