**Using area to solve problems :**

We may need the area of different figures to solve many real-world problems.

In this section, we are going to see, how area of figures can be used to solve real world problems.

**Example 1 : **

A banquet room is being carpeted. A floor plan of the room is shown below. Each unit represents 1 yard. The carpet costs $23.50 per square yard. How much will it cost to carpet the room ?

**Solution :**

**Step 1 : **

Separate the composite figure into simpler shapes as shown by the dashed lines : a parallelogram, a rectangle, and a triangle.

**Step 2 : **

Find the area the parallelogram.

Base (b) = 4 yards

Height (h) = 2 yards

Use the formula.

A = bh

A = 4 · 2

A = 8 square yd

The area of the parallelogram is 8 square yards.

**Step 3 : **

Find the area the rectangle.

Length (l) = 6 yards

Width (w) = 4 yards

Use the formula.

A = lw

A = 6 · 4

A = 24 square yd

The area of the rectangle is 24 square yards.

**Step 3 : **

Find the area the triangle.

Base (b) = 1 yard

Height (h) = 2 yards

Use the formula.

A = (1/2) bh

A = (1/2)(1)(2)

A = 1 square yd

The area of the triangle is 1 square yard.

**Step 4 : **

Find the area of the composite figure.

A = 8 + 24 + 1 = 33 square yards

**Step 4 : **

Calculate the cost to carpet the room.

Total cost = Area · Cost per yard

Total cost = 33 · $23.50

Total cost = $775.50

Hence, the cost to carpet the banquet room is $775.50.

**Example 2 :**

A window is being replaced with tinted glass. The plan at the right shows the design of the window. Each unit length represents 1 foot. The glass costs $28 per square foot. How much will it cost to replace the glass? Use 3.14 for π.

**Solution : **

**Solution :**

**Step 1 : **

Separate the composite figure into simpler shapes as shown by the dashed lines : a rectangle, two semicircles with equal area (one is one the left side of the rectangle and other one is on the right side).

**Step 2 : **

Find the area the rectangle.

Length (l) = 5 ft

Width (w) = 4 ft

Use the formula.

A = lw

A = 5 · 4

A = 20 square ft

The area of the rectangle is 24 square feet.

**Step 3 : **

Find the combined area of two semi-circles.

Radius = 2 ft

Use the formula.

A = 2 x (1/2)πr²

A = πr²

A = (3.14)(2)²

A = (3.14)(4)

A = 12.56 square ft

The combined area of two semi circles is about 12.56 square ft.

**Step 4 : **

Find the area of the composite figure.

A = 20 + 12.56 = 32.56 square ft

**Step 5 : **

Calculate the cost of tinted glass for the window.

Total cost = Area · Cost per feet

Total cost = 32.56 · $28

Total cost = $911.68

Hence, the cost of tinted glass for the window is $911.68.

After having gone through the stuff given above, we hope that the students would have understood "Using area to solve problems ".

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