Question

The area of an isosceles trapezoid is 72m2 and its diagonals are perpendicular. Find the length of a diagonal.

Answer 1

The area of a triangle with a base of 166 mm and a height of 930.0 mm is 0.077 m² when expressed with three significant figures after converting from millimeters to meters.

Step-by-step explanation:

The area of an isosceles trapezoid with perpendicular diagonals can be found using the property of right triangles. However, the area of a triangle is given by the formula ½ × base × height. If we have the base as 166 mm and height as 930.0 mm, converting these to meters first (1 m = 1000 mm), we get base = 0.166 m and height = 0.930 m. The area in square meters of this triangle would be:

Area = ½ × 0.166 m × 0.930 m

Area = 0.07719 m2

To express the answer to the proper number of significant figures, we observe that the least number of decimal places in the given measurements is two, so the area, while calculated as 0.07719 m2, is rounded to 0.077 m2 with three significant figures.

Answer 2

We are given the area of an isosceles trapezoid which is 72 m^2 and its diagonals are perpendicular. We need to find the length of a diagonal.

The formula for the area of an isosceles trapezoid is:

A = 1/2 (b1+b2) h

Solve for the sides and the bases of the trapezoid and then solve for the length of the diagonal,

d = √((b1 * b2) + h^2)