Subjects geometry

Composite Area 30E22C

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1. **State the problem:** Calculate the area of the composite shape that looks like a right-pointing arrow with given dimensions: height 6 ft on the left, width 7 ft at the bottom, vertical segments of 3 ft at top right and bottom right, and a 4 ft horizontal extension at the arrowhead. 2. **Approach:** Break the composite shape into simpler shapes whose areas we can calculate easily, then sum or subtract these areas. 3. **Identify shapes:** - A large rectangle on the left side with height 6 ft and width 3 ft (since the vertical segments on the right are 3 ft each, the remaining width on the left is 7 ft - 4 ft = 3 ft). - A smaller rectangle on the right bottom with height 3 ft and width 3 ft. - A triangle forming the arrowhead with base 4 ft and height 3 ft. 4. **Calculate areas:** - Area of left rectangle: $6 \times 3 = 18$ ft$^2$ - Area of bottom right rectangle: $3 \times 3 = 9$ ft$^2$ - Area of arrowhead triangle: $\frac{1}{2} \times 4 \times 3 = 6$ ft$^2$ 5. **Sum areas:** Total area = $18 + 9 + 6 = 33$ ft$^2$ 6. **Answer:** The area of the composite shape is **33 square feet**.