Question

1. Find the area of parallelogram ABCD.

Round to the nearest tenth.

A 55.4 m2

C 69.3 m2

B 60 m2

D 80 m2

2. The area of the parallelogram DEFG is 143 square units.

Find the height. Round to the nearest tenth if necessary.

Fll units

H 22 units

G 14.3 units

J 44 units

3. The base of a triangle is three times its height.

If the area of a triangle is 54 square inches, find its height.

A 18 in.

C3 in.

B 6 in.

DI in.

4. Find the area of quadrilateral PQRS.

F 34.1 units

G 65 units?

H 130 units?

J 360 units

Answer 1

1: C =69.3 m2

2: F = ll units

3. C: 3 in.

4. G =65 units

Explanation:

1: C =69.3 m2

We see from the figure that height of the parallelogram ABCD is not known and the base is 10 m

Taking the right angled triangle the height is given by

Sine theta= height/hypotenuse

height = hypotenuse* sine theta

= 8* sine 60

= 8* 0.866= 6.928

Area of parallelogram= base * height

= 10 * 6.928

= 69.28

=69.3 m²

2: F = ll units

We see from the figure that height of the parallelogram DEFG is not known and the base is 13 cm

Area of parallelogram= base * height

143 = 13 * height

Height = 143/13= 11 units

3. C: 3 in.

The area of the triangle = 1/2 * base * height

Let the height be x then the base is 3x

54= 1/2*x*3x

54= 3x²/2

27= 3x²

x²=27/3

x²= 9

x= 3

The height is 3 inches

4. G =65 units

Area of the quadrilateral = 1/2 *PR*QO + 1/2 *PR*OS

= 1/2*13*4+ 1/2*13*6

=26+ 39

= 65 units

These measurements are given in the diagram .