Question

1. Trapezoid BEAR has a height of 8.5 centimeters and parallel bases that measure 6.5 centimeters and 11.5 centimeters. To the nearest square centimeter, find the area of the trapezoid.
Area of trapezoid BEAR = ___________ square centimeters

2. Regular pentagon PENTA has side lengths that are 9 meters long. To the nearest square meter, find the area of the pentagon.

Area of pentagon PENTA = _____square centimeter

Answer 1

Given

1) Trapezoid BEAR with bases 11.5 and 6.5 and height 8.5, all in cm.

2) Regular pentagon PENTA with side lengths 9 m

Find

The area of each figure, rounded to the nearest integer

Solution

1) The area of a trapezoid is given by

... A = (1/2)(b1 +b2)h

... A = (1/2)(11.5 +6.5)·(8.5) = 76.5 ≈ 77

The area of BEAR is about 77 cm².

2) The conventional formula for the area of a regular polygon makes use of its perimeter and the length of the apothem. For an n-sided polygon with side length s, the perimeter is p = n·s. The length of the apothem is found using trigonometry to be a = (s/2)/tan(180°/n). Then the area is ...

... A = (1/2)ap

... A = (1/2)(s/(2tan(180°/n)))(ns)

... A = (n/4)s²/tan(180°/n)

We have a polygon with s=9 and n=5, so its area is

... A = (5/4)·9²/tan(36°) ≈ 139.36

The area of PENTA is about 139 m².