The area of a right triangle is half the product of the lengths of its legs, so we need to use the Pythagorean Theorem to find the length of the other leg. Set \(\displaystyle c = 39 , b = 36\):

\(\displaystyle a^{2} = c^{2} - b^{2}\)

\(\displaystyle a^{2} = 39 ^{2} - 36^{2}\)

\(\displaystyle a^{2} = 1,521 - 1,296\)

\(\displaystyle a^{2} = 225\)

\(\displaystyle a = \sqrt{225} = 15\)

The legs have length \(\displaystyle 15\) and \(\displaystyle 36\) feet; multiply both dimensions by \(\displaystyle 12\) to convert to inches:

\(\displaystyle 15 \times 12 = 180\) inches

\(\displaystyle 36 \times 12 = 432\) inches.

Now find half the product:

\(\displaystyle A = \frac{1}{2} \cdot 180 \cdot 432 = 38,880\ in^{2}\)

Multiply each dimension by \(\displaystyle 100\) to convert meters to centimeters:

\(\displaystyle 4.3 \times 100 = 430\)

\(\displaystyle 3.5 \times 100 = 350\)

Multiply these dimensions to get the area of the rectangle in square centimeters:

\(\displaystyle 430 \times 350 = 150,500\textrm{ cm}^{2}\)

The length of a leg of \(\displaystyle \Delta ECM\) is equal to the height of the orange region, which is a trapezoid. Call this length/height \(\displaystyle h\).

Since the triangle is isosceles, then \(\displaystyle CM = h\), and since \(\displaystyle M\) is the midpoint of \(\displaystyle \overline{CT}\), \(\displaystyle MT = h\). Also, since opposite sides of a rectangle are congruent, 

\(\displaystyle RE = CT = CM + MT = h + h = 2h\)

Therefore, the orange region is a trapezoid with bases \(\displaystyle h\) and \(\displaystyle 2h\) and height \(\displaystyle h\). Its area is 72, so we can set up and solve this equation using the area formula for a trapezoid:

 \(\displaystyle \frac{1}{2} (B + b)h = 72\)

\(\displaystyle \frac{1}{2} (2h + h)h = 72\)

\(\displaystyle \frac{1}{2} (3h )h = 72\)

\(\displaystyle \frac{3}{2}h^{2} = 72\)

\(\displaystyle \frac{3}{2}h^{2} \cdot \frac{2}{3} = 72 \cdot \frac{2}{3}\)

\(\displaystyle h^{2}= 48\)

\(\displaystyle h = \sqrt {48}\)

This is the length of one leg of the triangle.

Use the following formula, with \(\displaystyle B = 36,b = 24,h=25\):

\(\displaystyle A = \frac{1}{2} (B+b)h = \frac{1}{2} (36+24) \cdot 25 = 750\)

The formula for the area of a triangle is \(\displaystyle \dpi{100} Area=\frac{1}{2}\times base\times height\).

Plug the given values into the formula to solve:

\(\displaystyle \dpi{100} Area=\frac{1}{2}\times 12\times 3\)

\(\displaystyle \dpi{100} Area=\frac{1}{2}\times 36\)

\(\displaystyle \dpi{100} Area=18\)

To solve, simply use the formula for the area of a square. Thus,

\(\displaystyle A=s^2=1^2=1\)

To solve, simply use the formula for the area of a triangle.

Given the height is 6 and the base is 3, substitute these values into area of a triangle formula.

Thus,

\(\displaystyle A=\frac{1}{2}Bh=\frac{1}{2}*6*3=9\)

The area of a square, it being a rhombus, is the product of the lengths of its diagonals. The diagonals are of the same length, so both diagonals have length 8, and the area of the square is

\(\displaystyle \frac{1}{2} \times 8^{2} = \frac{1}{2} \times 8 \times 8 = 32\).

60% of 32 is equal to 32 multiplied by \(\displaystyle \frac{60}{100}\), which is

\(\displaystyle 32 \times \frac{60}{100} = 32 \times \frac{3}{5} = 19\frac{1}{5}\).

The area of a circle with radius \(\displaystyle r\) is 

\(\displaystyle A = \pi r^{2}\).

The radius of the circle is\(\displaystyle r=12\), so the area is

\(\displaystyle A = \pi \cdot 12^{2} = 144 \pi\).

40% of this is 

\(\displaystyle 144 \pi \cdot \frac{40}{100} = 144 \pi \cdot \frac{2}{5 }= \frac{288 \pi}{5}\)

Convert each dimension from feet to yards by dividing by conversion factor 3:

\(\displaystyle 6 \textup{ ft} \div 3 \textup{ yd/ft} = 2 \textup{ yd}\)

\(\displaystyle 4 \frac{1}{2} \textup{ ft} \div 3 \textup{ yd/ft} = \frac{9}{2} \textup{ ft} \div 3 \textup{ yd/ft}= \frac{3}{2} \textup{ yd}\)

Their product is the area in square yards:

\(\displaystyle 2 \textup{ yd} \times \frac{3}{2} \textup{ yd} = 3 \textup{ yd} ^{2}\).