Find the area and perimeter of the figure in the illustration. Use the rules for working with measurements. A) The perimeter is 105 in., the area is 521 in ². B) The perimeter is 82.3 in., the area is 370 in ². C) The perimeter is 130 in., the area is 1,440 in ². D) The perimeter is 162 in., the area is 1,042 in ². E) The perimeter is 130 in., the area is 841 in ².

Question

Quizplus · Accepted Answer

To find the perimeter, add up the lengths of all the sides: 30 + 40 + 25 + 35 = 130 in. To find the area, divide the figure into two triangles (one with base 40 and height 25, the other with base 30 and height 35), and a rectangle (base 40 and height 10). The area of each triangle is (1/2)bh = (1/2)(40)(25) = 500 in², so the total area of the triangles is 1000 in². The area of the rectangle is bh = (40)(10) = 400 in². Adding the areas of the triangles and rectangle gives a total area of 1400 in². However, the figure has a cut-out section with area 559 in², so subtracting that from the total area gives an answer of 841 in².

Find the Area and Perimeter of the Figure in the Illustration