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The Pythagorean Theorem
The area of triangles
Quadrilaterals
Area of quadrilaterals
100

A right triangle has legs 9 cm and 12 cm.
Find the hypotenuse.

15 cm

100

Base = 14 cm, height = 5 cm.
Find the area.

35 cm2

100

A quadrilateral has 4 right angles.
Name it.

Rectangle

100

A parallelogram has base 18 cm and height 7 cm.
Find the area.

126 cm2

200

The hypotenuse of a right triangle is 17 cm, one leg is 8 cm.
Find the other leg.

15 cm

200

A right triangle has legs 6 cm and 11 cm.
Find the area.

33 cm2

200

A quadrilateral has exactly one pair of parallel sides.
Name it.

Trapezium

200

A rhombus has diagonals 16 cm and 30 cm.
Find the area.

240 cm2

300

A rectangle is 7 cm wide and its diagonal is 25 cm.
Find its length.

24 cm

300

The base of a triangle is 18 cm.
Its area is 72 cm².
Find the height.

8 cm

300

A quadrilateral has two pairs of parallel sides and all sides are equal.
Name it.

Rhombus

300

In a parallelogram one angle is 70°.

a) Find the other angles.
b) If the base is 12 cm and height is 5 cm, find the area.

a. 70°, 110°, 70°, 110°

b. 60 cm2

400

An isosceles triangle has equal sides 10 cm and base 16 cm.
Find the height belonging to the base.

6 cm

400

The base of an isosceles triangle is 12 cm, its legs are 10 cm.

a) How long is the altitude belonging to the base?
b) Calculate the area.

a. 8 cm

b. 48 cm2

400

The ratio of the angles of a quadrilateral is 4:5:6:9. Calculate the measure of its angles.

60°, 75°, 90°, 135°

400

A rhombus has side 13 cm and one diagonal 10 cm.

a) Find the other diagonal.
b) Find the area.

a. 24 cm

b. 120 cm2

500

A trapezium has bases 10 cm and 26 cm.
The non-parallel sides are both 13 cm.

Find the height.

10.25 cm

500

The base of an isosceles triangle is 8 cm, its legs are 15 cm.

a) Find the altitude belonging to the base.
b) Calculate the area.
c) Find the altitude belonging to the legs.

a. 10.46 ~ 10.5 cm

b. 57.8 cm2

 c. 7.7 cm
500

In a quadrilateral, two opposite angles are equal, their sum 140°. The other two angles are in the ratio 3:5. Give the measure of the angles. 

70°, 70°, 82.5°, 137.5°

500

An isosceles trapezium has bases 14 cm and 24 cm.
The legs are 13 cm.

a) Find the height.
b) Find the area.

a. 12 cm

b. 228 cm2