## Metric Problems

Problem: What is the area of a triangle (ha) with a base 150.0 m long and a height of 100.0 m?

Solution:

10,000 m2

Problem: Determine the area (m2) for a triangle having sides measuring 650.0 m, 428.0 m, and 282.0 m.

Solution:

A = 7680.0 (680.0 - 650.0) (680.0 - 428.0) (680.0 - 282.0)

= V2046038400

= 45,233.15598 or 45,230 m2

Problem: Determine the area (m2) of a triangle with sides of 350.0 m and 555.0 m and an included angle of 45°.

Solution:

A=-xaxbx sine 0 = - x 350.0 m x 555.0 m x sine 45 22

194250 2

Problem: What is the area (m2) of a rectangle measuring 1320.0 m by 660.0 m?

Solution:

Problem: What is the area (ha) of a parallelogram where the base measures 1,050.0 m, and the height measures 750.0 m?

Solution:

1 ha 1 ha A (ha) = b x h x -2 = 1,050.0 m x 750.0 m x

10,000 m2 10,000 m2

787500

10000

Problem: Find the area of a circle (m2) having a radius of 75.0 m.

Solution:

A (m2) = n x r2 = 3.14... x 75.02 = 17671.45... or 17,700 m2

Problem: Find the area of a sector (m2) having a radius of 135.0 m and an angle of 60.0°.

Solution:

3,433,590 2

Problem: What is the area of a sector (ha) if the radius is 100.0 m and the arc length is 210.0 m?

 1 \ , -1 1 1 1 1 1 1 1 1 1 1 1 1 FIGURE 13.19. Metric example of using trapezoids for irregular shape. 400 m 200 m 300 m FIGURE 13.19. Metric example of using trapezoids for irregular shape. Solution: 2 10,000 m2 2 10,000 m2 10,000 Problem: What is the area (ha) of a trapezoid with parallel sides of 300.0 m and 450.0 m, and with a height of 120.0 m? Solution: 43,560 ft2 ,'300.00 ft + 450.00 ft \ 1 ac = 120.0 ft x I -?- I x 43,560 ft2 43,560 ft2 Problem: What is the area (acres) for the field illustrated in Figure 13.19? Solution: The total area (AT) is the sum of each trapezoidal shape (dashed lines). FIGURE 13.20. Summation trapezoidal equation applied to a metric measured field. 1 ha 10,000 m2 A (ha) = _ 1 "" 2 x 33,8750 ft2 = 33.875 or 33.9 ha Problem: Determine the area (ac) of the irregular-shaped field illustrated Figure 13.20. Solution: 500 m = 200 m x i + (450 m + 390 m + 275 m + 370 m + 390 m) = 200 m x (250 m + 450 m + 390 m + 275 m + 370 m + 390 m + 200 m) 10,000 m2