Thursday

September 18, 2014

September 18, 2014

Posted by **Katreena** on Sunday, May 5, 2013 at 3:30am.

- solid mensuration -
**dlsu**, Tuesday, October 15, 2013 at 2:29am1405

- geometry -
**drowranger766**, Wednesday, October 16, 2013 at 9:39amSince the angle of intersection of the diagonals is 70 degrees then the other angle of intersection of the diagonals is 110 degrees.

180 = 70 + θ

where θ = the other angle of intersection

θ = 110 degrees

A parallelogram makes 4 oblique triangles. One triangle has angles : 30, 40, and 110 degrees.

Since the diagonals intersect at their midpoints, the length of a side of one oblique triangle will measure 31 degrees (which is from 62/2).

By the given values you can solve for half the length of the shorter diagonal using the law of sines.

31/sin40 = x/sin30

where x = the length of one side of the oblique triangle and also half the length of the shorter diagonal.

x = 24.11371932 cm

2(24.11371932) = 48.23 --> length of shorter diagonal

use the formula:

Area of parallelogram = (lenth of longer diagonal x lenth of shorter diagonal x sinθ)/2

where θ = angle of intersection of the two diagonals (either 70 degrees or 110 degrees)

A = ((62 cm)(48.23)sin70)/2

A = 1404.962628 or 1405 cm^2

**Answer this Question**

**Related Questions**

geometry theorems - I have six questions which will be on a test two weeks from ...

Geometry - find the area of a parallelogram with diagonals of lengths 10 inches ...

geometry - find the area of a parallelogram with diagonals of lengths 10 inches ...

Math - the distance between the center of symmetry of a parallelogram and its ...

Trig - The diagonals of a parallelogram intersect at a 42◦ angle and have ...

Pre-calculus - Find the lengths of the diagonals of a parallelogram with ...

geometry - in a parallelogram, consecutive angles aresupplementary. in the ...

maths - A parallelogram has two adjacent sides of length 4cm and 6cm ...

geometry - In parallelogram ABCD, BC = 8, DC = 12, and measure of angle D is 50 ...

geometry - Given: QRST is a parallelogram. Prove: QRST is a square. Complete ...