Angles and Areas of Polygons

Polygon Angles

100

Find the sum of the interior angles in a pentagon.

(n-2)180 = (5-2)180 = 3*180 =

540 degrees

200

Find the measure of each interior angle in a hexagon.

(6-2)*180 divided by 6 = 4*180/6 =

120 degrees

300

What is the sum of the exterior angles of a decagon.

360 degrees

400

What is the measure of each exterior angle of a heptagon?

360/7 =

51.4 degrees

500

If the angles of a pentagon are 100 degrees, 50 degrees, a right angle, and x and x+6, find the value of x.

100+50+90+x+x+6=540 

2x=294 

x=147

Find Area

100

Find the area of a rectangle with dimensions: 5 ft and 7 ft.

35 ft²

200

Find the area of a parallelogram with a base of 9in and a height of 10in.

90 in²

300

Find the area of a rhombus with a diagonal of 6m and each side length of the rhombus is 5m.

24m²

400

Find the area of a trapezoid with bases of 15ft 8ft and height of 4ft.

46m²

500

Find the area of a shape that has a rectangle with a triangle on top of it. Dimensions of the rectangle are 5 ft high by 10 ft wide. The height of the triangle is 4 ft.

70 ft²

Find Dimensions

100

The area of a parallelogram is 68ft². The base is 10ft. What is the height of the parallelogram?

6.8ft

200

The area of a square is 144 ft². What are the measures of the sides of the square?

12 ft each

300

The area of a trapezoid is 40 in² and the bases of the trapezoid are 6 in and 10 in. What is the height of the trapezoid?

5 in

400

The area of a triangle is 40 ft² and the base of the triangle is 10 ft. What is the height of the triangle?

8 ft

500

Area of a trapezoid is 36m². The height of the trapezoid is 4m and the shorter base is 6m long. What is the length of the longer base?

12m

Circles

100

Find the circumference of a circle with a diameter of 6 ft. Round answer to the nearest tenth.

9*pi or 28.3 ft

200

What is the circumference of a circle with a radius of 4 in?

8*pi or 25.1 in

300

What is the area of a circle with a diameter of 14m?

49*pi or 153.9 m²

400

What is the area of the sector of a circle with a 18 degree angle and a radius of 6m?

(18/360)*pi*6^2 = 5.7m²

500

If the area of a circle is 44 ft², what is the radius?

3.7 ft

Misc

100

If the circumference of a circle is 20 m, what is the radius?

3.2 m

200

What is the interior angle of a regular nonagon?

140 degrees

300

If the exterior angle of a regular polygon is 20 degrees, how many sides does the polygon have?

360/20 = 18 sides

400

If the area of a circle is 78 m², what is the circumference?

31.3 m

500

What is the exterior angle of 52-sided regular shape?

6.9 degrees