Let's analyze the problem step-by-step to find the total number of 8-inch-high by 16-inch-long bricks/blocks needed to complete the wall. --- # Step 1: Understand the problem - **Wall length:** 80 feet - **Brick size:** 8 inches high x 16 inches long - **Wall height (from figure):** 17'-4" (which is 17 feet + 4 inches) - **Overhead door width:** 12 feet (not relevant for brick calculation) - **Mortar joints:** .8 inches thick (per joint) - **Goal:** Determine how many bricks/blocks are needed --- # Step 2: Convert all measurements to consistent units (inches) | Measurement | Conversion | Value in inches | |--------------|--------------|-----------------| | Wall length | 1 foot = 12 inches | 80 ft × 12 = **960 inches** | | Wall height | 17 ft 4 in | (17 × 12) + 4 = 204 + 4 = **208 inches** | | Brick height | 8 inches | 8 inches | | Brick length | 16 inches | 16 inches | | Mortar joint thickness | .8 inches | .8 inches | --- # Step 3: Account for mortar joints - The **actual brick height** including mortar joints is: \[ \text{Brick height} + \text{mortar joint} = 8 + .8 = 8.8 \text{ inches} \] - The **actual brick length** including mortar joints (assuming joints are between bricks in the same row) is: \[ 16 + .8 = 16.8 \text{ inches} \] However, since mortar joints are between bricks, the total length of a row is: \[ \text{Number of bricks} \times \text{brick length} + (\text{number of joints} \times \text{joint thickness}) \] But for simplicity, we can treat each brick as including the joint spacing, or consider that the joints are between bricks. --- # Step 4: Calculate the number of rows of bricks vertically - Total wall height: 208 inches - Height of each brick row (including mortar joint): 8.8 inches Number of rows: \[ \frac{208}{8.8} \approx 23.64 \] Since we can't have a fraction of a row, round up: \[ \boxed{24 \text{ rows}} \] --- # Step 5: Calculate the number of bricks per row horizontally - Total wall length: 960 inches - Length of each brick including joint (assuming joints are between bricks): 16.8 inches - Number of bricks per row: \[ \frac{960}{16.8} \approx 57.14 \] Round to the next whole number: \[ \boxed{58 \text{ bricks per row}} \] --- # Step 6: Calculate total bricks needed Total bricks: \[ \text{Number of rows} \times \text{bricks per row} = 24 \times 58 = 1392 \] --- # **Final Answer:** \[ \boxed{\textbf{1392 bricks}} \] This is the estimated number of 8-inch-high by 16-inch-long bricks (with mortar joints) required to complete the wall.

In this calculation, the total number of bricks was calculated without deducting the area occupied by oversized doors because the problem statement did not specify that the doors should be accounted for in the quantity of bricks needed. If the doors are part of the wall area, they should indeed be deducted. Let's refine the calculation by including the door size: --- # Step 1: Understand the door dimensions - **Door width:** 12 feet - **Door height:** Assume standard door height of 7 feet (84 inches) unless specified otherwise. --- # Step 2: Convert door dimensions to inches | Measurement | Conversion | Value in inches | |--------------|--------------|-----------------| | Door width | 12 ft × 12 = 144 inches | **144 inches** | | Door height | 7 ft × 12 = 84 inches | **84 inches** | --- # Step 3: Calculate the area of the door - **Door area**: \[ \text{Area} = \text{width} \times \text{height} = 144 \text{ inches} \times 84 \text{ inches} = 12,096 \text{ square inches} \] --- # Step 4: Calculate the total area of the wall - **Wall area**: \[ \text{Wall area} = \text{length} \times \text{height} = 960 \text{ inches} \times 208 \text{ inches} = 199,680 \text{ square inches} \] --- # Step 5: Deduct the door area from the wall area - **Net wall area**: \[ \text{Net wall area} = \text{Wall area} - \text{Door area} = 199,680 - 12,096 = 187,584 \text{ square inches} \] --- # Step 6: Calculate the area of each brick - **Brick area**: \[ \text{Brick area} = \text{height} \times \text{length} = 8 \text{ inches} \times 16 \text{ inches} = 128 \text{ square inches} \] --- # Step 7: Calculate the total number of bricks needed - **Total bricks**: \[ \text{Total bricks} = \frac{\text{Net wall area}}{\text{Brick area}} = \frac{187,584}{128} \approx 1464 \] --- # **Final Answer:** \[ \boxed{\textbf{1464 bricks}} \] This updated calculation accounts for the oversized door, providing a more accurate estimate of the number of bricks required for the wall.