Grade 7 / Size 14 exercises (100% corrected)

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ABCDE2;5cm4cm ABCMNIhb ABC 1. Duration and schedule E.5626 1 A train departs from Sète station at 14 h 34 min and trav-els to Paris. The travel time is 3 h 42 min . What is the arrival time of the train in Paris station. 2 For his training, a runner runs a 2 h 25 min course daily. If he starts his run at 8 h 30 min at what time will he finish his training? 2. Perimeter E.5627 Consider the polygon AEBCD shown below where the quadrilateral ABCD is a parallelo-gram and where the triangle ABE is an equilateral triangle. Determine the perimeter of the polygon AEBCD . 3. Areas of a triangle E.1414 Let ABC be any triangle. Consider the points M and N such that : ABNM be a rectangle; C belongs to segment [ MN ] . We note I the foot of the triangle height ABC arising from C , and h the length of the height [ CI ] and b the length of the associated base : here the segment [ AB ] . 1 a Compare the area A ACI of the triangle ACI and the area A AICM of the rectangle AICM . b Deduce the value of A ACI as a function of h and AI 2 Give the value of A BCI as a function of h and BI . 3 As a function of b and h , give the expression for the area A ABC . E.1413 Consider the ABC triangle shown below : 1 a In the triangle ABC opposite, draw the point H foot of the height from the vertex B b By measuring the lengths BH and AC , determine the area of triangle ABC . 2 a Plot the height from C . b Also calculate the area of triangle ABC using the height from C . E.1411 Let ABO be a right triangle at O and [ OM ] the height from O . 1 Draw a representation of this configuration. 2 Derive the equality: AB × OM = OA × OB 4. Area of the parallelogram https://chingmath.fr chapExoCorrec/5626 sacados/5626 chapExoCorrec/5627 sacados/5627 ABCDE2;5cm4cm chapExoCorrec/1414 sacados/1414 ABCMNIhb chapExoCorrec/1413 sacados/1413 ABC chapExoCorrec/1411 sacados/1411
ABCD ABCD ABC4cm3cm5cmHIJK3;5cm5cm4cm DEFG2;4cm1;8cm3cm4cm1;4cm3cm4;5cm2cmONML 12cm0;75cm E.5629 Consider the parallelogram below : 1 a Using the square, draw the line ( d ) perpendicular to the line ( AB ) and through the point D . The line ( d ) intercepts the line ( AB ) at point H . b Using the square, draw the line (Δ) perpendicular to the line ( DC ) through the point B . The line (Δ) in-tercepts the line ( DC ) at point I . 2 Give the nature of the following polygons: ADH ; DHBI ; BIC 3 Using the graduated ruler, make the measurements neces-sary to determine the area of the parallelogram ABCD . E.5630 We consider the parallelogram rep-resented below : 1 a Draw the diagonal [ AC ] of the parallelogram ABCD . b Using the square, draw the line ( d ) through the point B and perpendicular to the line ( AC ) . The line ( d ) intercepts the line ( AC ) at point H . c Using the square, draw the line (Δ) through the point D and perpendicular to the line ( AC ) . The line (Δ) intercepts the line ( AC ) at point I . 2 Using the graduated ruler and making the necessary measurements, determine the area of the parallelogram ABCD . 5. Area of the parallelogram E.1409 For each of the figures below, calcu-late their areas using the general formulas and your calcula-tions : Note: HIJK is a parallelogram, LMNO is a trapezoid. 6. Disc area E.8033 ˇ A DVD (Digital Versatile Disc) is an optical disc used for backing up and storing data in digital form. ı (source: Wikipedia) It consists of a plastic part with a diameter of 12 cm and a central hole with a radius of 0.75 cm . Determine the surface area of the plastic used to make this DVD, rounded to the nearest hundredth of a square centime-ter. Hint: we will use : ı ≈ 3.14 7. Area of a compound figure https://chingmath.fr chapExoCorrec/5629 sacados/5629 ABCD chapExoCorrec/5630 sacados/5630 ABCD chapExoCorrec/1409 sacados/1409 ABC4cm3cm5cmHIJK3;5cm5cm4cm DEFG2;4cm1;8cm3cm4cm1;4cm3cm4;5cm2cmONML chapExoCorrec/8033 sacados/8033 12cm0;75cm
ABCO6cm3;2cm6;8cm ABCD ABCDEF E.1410 Calculate the area of the figure opposite, composed of a right-angled triangle ABC and a half-disk with diameter [ AB ] , rounded to the nearest mm 2 . Hint: ı ≈ 3.14 E.4631 The square ABCD has side 4 cm . The hatched portion is bounded by two circles of radii 4 cm and respective centers A and C . Determine the area of the hatched portion. 8. Reminders on volumes E.6585 In the table below, for each line, re-trieve the volume value shown on the left and convert it to the unit shown on the right : km 3 hm 3 dam 3 m 3 dm 3 cm 3 mm 3 312 m 3 . . . dm 3 0.32 dm 3 . . . m 3 350 mm 3 . . . m 3 2 ‘ . . . m 3 33 c‘ . . . cm 3 25 km 3 . . . m 3 We recall the equality : 1 ‘ =1 dm 3 9. Volume of parallelepipeds E.7975 Consider the solid below formed by two cubes : the larger cube has side 8 cm , the side of the second cube measures half a side of the first cube. 1 Determine the volume of this solid. 2 Determine the area of the outer surface of this solid. 10. Volume of straight prisms E.7976 Consider the right prism ABCDEF shown below whose base ABC is a right-angled triangle at A : https://chingmath.fr chapExoCorrec/1410 sacados/1410 ABCO6cm3;2cm6;8cm chapExoCorrec/4631 sacados/4631 ABCD chapExoCorrec/6585 sacados/6585 chapExoCorrec/7975 sacados/7975 chapExoCorrec/7976 sacados/7976 ABCDEF
We give the following measurements : AC = 1.6 cm ; AB = 6.5 cm ; AD = 3 cm Determine the volume of the right prism ABCDEF . https://chingmath.fr