Examples with solutions for Area of a Deltoid: Using ratios for calculation

Exercise #1

The main diagonal of the deltoid shown below is 39 cm long.

The length of the secondary diagonal is 14 cm.

The secondary diagonal divides the main diagonal in the ratio of 8:5.

Calculate the ratio of the two isosceles triangles whose common base is the secondary diagonal.

393939141414AAABBBCCCDDD

Video Solution

Answer

8:3 8:3

Exercise #2

The length of the main diagonal in a deltoid is 25 cm.

The length of the secondary diagonal in the deltoid is 9 cm.

The secondary diagonal divides the main diagonal in a ratio of 3:2.

Find the ratio of the two isosceles triangles whose common base is the secondary diagonal.

252525999AAABBBCCCDDD

Video Solution

Answer

2:3 2:3

Exercise #3

The length of the main diagonal in the deltoid is equal to 30 cm

The length of the secondary diagonal in the deltoid is equal to 11 cm

The secondary diagonal divides the main diagonal in the ratio of 4:2

Find the ratio of the areas of the two isosceles triangles whose secondary diagonal is their common base.

303030111111AAABBBCCCDDD

Video Solution

Answer

2:1 2:1

Exercise #4

The main diagonal of a deltoid is 28 cm long.

The length of the secondary diagonal is equal to 13 cm.

The secondary diagonal divides the main diagonal in the ratio of 4:3.

Calculate the ratio between the two isosceles triangles whose common base is the secondary diagonal.

282828131313AAABBBCCCDDD

Video Solution

Answer

4:3 4:3

Exercise #5

The length of the main diagonal in the deltoid is equal to 42 cm.

The secondary diagonal divides the main diagonal in the ratio of 6:1

The area of the small isosceles triangle, whose secondary diagonal forms its base, is equal to 18 cm².

Find the length of the secondary diagonal.

S=18S=18S=18424242AAABBBCCCDDD

Video Solution

Answer

6 6

Exercise #6

A deltoid has a main diagonal measuring 30 cm.

The secondary diagonal divides the main diagonal in a ratio of 3:2.

The area of the small isosceles triangle, the base of which is formed by the deltoid's secondary diagonal, is 42 cm² long.

Calculate the length of the secondary diagonal.

S=42S=42S=42303030AAABBBCCCDDD

Video Solution

Answer

7 7

Exercise #7

The length of the main diagonal in the deltoid is equal to 42 cm.

The secondary diagonal divides the main diagonal in the ratio of 5:1

The area of the small isosceles triangle, whose secondary diagonal forms its base, is equal to 12 cm².

Find the length of the secondary diagonal.

S=12S=12S=12424242AAABBBCCCDDD

Video Solution

Answer

4 4

Exercise #8

The length of the main diagonal in the deltoid is equal to 40 cm.

The secondary diagonal divides the main diagonal in the ratio of 7:1

The area of the small isosceles triangle, whose secondary diagonal forms its base, is equal to 20 cm².

Find the length of the secondary diagonal.

S=20S=20S=20404040AAABBBCCCDDD

Video Solution

Answer

8 8

Exercise #9

Given the deltoid ABCD

and the deltoid AFCE whose area is 20 cm².

The ratio between AO and OC is 1:3

the angle ADC⦠. is equal to the angle ACD⦠.

AD is equal to 8

888DDDCCCAAABBBOOOFFFEEE

Calculate the area of the triangle CEF

Video Solution

Answer

15 cm²

Exercise #10

The deltoid ABCD is shown below.

The ratio between CK and AC is 1:3.

Calculate the ratio between triangle ACD and triangle BAD.AAABBBDDDCCCKKK

Video Solution

Answer

1:4

Exercise #11

Look the deltoid ABCD shown below.

The ratio between AO and OC is 1:5.

Calculate the ratio between triangle ABD and triangle BCD.

AAABBBCCCDDDOOO

Video Solution

Answer

1:5

Exercise #12

Shown below is the deltoid ABCD.

The ratio between triangle ABD and triangle BDC is 1:3.

Given in cm:

AO = 3

Calculate side OC.

333AAABBBCCCDDDOOO

Video Solution

Answer

9 cm