Exercise

1. In the figure below AD = 4, AB = 3 and CD = 9. What is the area of triangle AEC ?

A. 18 B. 13.5 C. 9 D. 4.5 E. 3

Exercise

In the figure below AD = 4, AB = 3 and CD

=9 .What is the area of triangle AEC?

∆ABE, ∆ DCE are similar with the ratio 1:3

AE : ED = 1:3

Area of ∆ AEC =

½AE . CD = 4.5

3

9

4

Exercise

2. Which of the following could be a value of x, in the diagram below?

A. 10 B. 20 C. 40 D. 50 E. any of the above

Exercise

2. Which of the following could be a value of x, in the diagram above?

90 < 5 x < 180

5( 10 = )50×

5( 20 = )100 √

Exercise

3. ABCD is a square of side 3, and E and F are the mid points of sides AB and BC respectively. What is the area of the

quadrilateral EBFD?

A. 2.25 B. 3 C. 4 D. 4.5 E. 6

Exercise

3. ABCD is a square of side 3, and E and F are the mid points of sides AB and BC respectively.

What is the area of the quadrilateral EBFD?

DE, DF are medians in

∆ABD, ∆ CBD

Area of ABCD = 9Area of EBFD ½ Area of ABCD

=4.5

1 23

4

Exercise

4. If the radius of the circle with centre O is 7 and the measure of angle AOB is 100, what is the

best approximation to the length of arc AB?

A. 9 B. 10 C. 11 D. 12 E. 13

Exercise

4. If the radius of the circle with centre O is 7 and the measure of angle AOB is 100, what is the

best approximation to the length of arc AB?

θ = Length of Arc = Area of sector 360 2π r π r 2

100( 2 x 22/7 x 7 /)360 =

4400/360 ≈ 12

Exercise

5. ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all equal. What is the

perimeter of the parallelogram?

A. 12 B. 9√3 C. 9 D. 8 E. 3√3

Exercise

5. ABCD is a parallelogram. BD = 2. The angles of triangle BCD are all equal. What is the

perimeter of the parallelogram?

∆BDC is an equilateral with side 2

Each 2 opposite sides

In a parallelogram are

=in length.

The perimeter = 8

Exercise

6. The slope of the line passing through the point )5,5( is 5/6. All of the following points could be on the line except

A. )2.5, 2( B. )11, 10( C. )8, 7.5( D. )-1, 0( E. )-7, -5(

Exercise

6. The slope of the line passing through the point )5,5( is 5/6. All of the following points could be on the line except

Slope=

5 - 2

5 – 2.5

=6/5

Y2 – Y1

X2 – X1

Exercise

7. PQRS is a parallelogram and ST = TR. What is the ratio of the area of triangle

QST to the area of the parallelogram?

A. 1 : 2 B. 1 : 3 C. 1 : 4 D. 1 : 5 E. it cannot be determined

Exercise

7. PQRS is a parallelogram and ST = TR. What is the ratio of the area of triangle

QST to the area of the parallelogram?

We have 4 equal Parts

SQT : PQRS =

1:4

Exercise

8. Two equal circles are cut out of a rectangle of card of dimensions 16 by 8. The circles have the maximum diameter possible. What is the approximate area of the paper remaining after

the circles have been cut out ?

A. 104 B. 78 C. 54 D. 27 E. 13

Exercise

The required region = large area – small area

Area of rectangle = length x width = 16 x 8 = 128

Area of circle = π r2

Diameter = 8, Radius = 4

3.14 x 42 ≈ 50 x 2 = 100

128 – 100 = 28

D is the most appropriate .

Exercise

9 .In the figure below, a circle with radius 7 cm is inscribed in a square. Find the area of the shaded region

Exercise

9 .In the figure below, a circle with radius 7 cm is inscribed in a square. Find the area of the shaded region

Area of square = s2 = 196

Area of circle = 22/7 x 49 = 154

The required area = 196 – 154

=42

Exercise

10 .In the figure below, a circle with radius of 7 cm is inscribed on a square. What is the perimeter of the blue region?

Exercise

10 .In the figure below, a circle with radius of 7 cm is inscribed on a square. What is the perimeter of the blue region?

Diameter = 14, side = 7√ 2

Perimeter of the square = 28 √ 2

Circumference of the circle=

44

Required perimeter = 28 √ 2 + 44

Exercise

11. If the central angle of the arc shown above is 60o ,and the radius of the circle is 7 cm long. Find the area of the sector.

Exercise

12. In the figure above if C is the mid-point of BD, and BC = AB. If the radius of the circle is 14 cm, find the length of

AD .Note: figure not drawn to scale

BD C

A

Exercise

13. If Mohamed moves 15 miles due east, then moves 12 miles due north, finally an additional 5 miles due east. What is the distance between the start point and the end

point?

Exercise.

14 .In the figure above. If D is the mid-point of AB, and DE // BC, if the area of the triangle ADE = 5 cm2. Find the area of the triangle ABC

A

BC

DE

Exercise

15. In the graph above, find the area of the rectangle.

O

(5 ,1)

(3 ,5)

EXERCISE

16 )Rectangle ABCD has

a perimeter of 26 .

The half circle with

diameter AD has an area of 8π. What is the perimeter of the part of the figure that is not

shaded?

A. 26 + 4π B. 18 + 8π C. 18 + 4π D. 14 + 4π E. 14 + 2π

EXERCISE

17 )AB and DE are parallel. Angle BAC = 30, angle CDE = 50. What is the measure of angle ACD

A. 100 B. 90 C. 80 D. 70 E. cannot be determined from the information

EXERCISE

18 )The solid brick shown is made of small bricks of side 1. When the large brick is disassembled into its component small bricks, the total surface area of all the small bricks is how much greater than the surface area of the

large brick ?A. 32 B. 40 C. 60 D. 72 E. 80

EXERCISE

19 )If the area of the right triangle above is 72, what is the value of x ?

EXERCISE

20 )The area of a rectangle with sides x and 3x, is how many times greater than the area of a right angled isosceles

triangle with side x?

EXERCISE

21) . In the figure above, AD = AC = CB. If the value of y is 28, what is the value of x?

EXERCISE

22 )What is the sum of x, y and z in the figure above ?

EXERCISE

23 )What is the area of the shaded region?

EXERCISE

24 )In the figure below, lines p and q are parallel. If point )x, y( lies on line q, which of the following represents the relationship between

x and y?

a. x + y = 0

b. x – y = 0

c. x + y = –1

d. x – y = –1

e. xy = –1