Summary work \# 5 Option I 1. The area of the triangle \( A B C \) is 10 cm 2 , and the length of the side \( A B \) is 5 cm . Calculate the length of the allowed height on the side \( A B \). 2. The perimeter of a rhombus is 40 cm , and the product of the lengths of the diagonals is 192 cm . Calculate the height of the rhombus. 3. The midpoint of the side \( A D \) of the parallelogram \( A B C D \) is \( E \). Calculate the area of the parallelogram if the area of the rectangle BCDE is 12 cm . 4. The area of the EFKT parallelogram is 72 cm . The point \( M \) lies on the line ET so that KM II FT. Calculate the area of the rectangle EFKM. 5. The acute angle of an isosceles trapezoid with bases 7 cm and 13 cm long is \( 45^{\circ} \). Calculate the area of the trapezoid.

To calculate the allowed height on side \( A B \) for triangle \( A B C \) with an area of 10 cm², you can use the formula \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \). By plugging in the numbers: \( 10 = \frac{1}{2} \times 5 \times \text{height} \), you can easily solve for the height, leading to a height of 4 cm. For the rhombus with a perimeter of 40 cm, each side measures 10 cm (40 cm ÷ 4). Using the relationship between the diagonals \( d_1 \) and \( d_2 \) of a rhombus (where the area equals \( \frac{1}{2} \times d_1 \times d_2 \)), set up the equation \( 192 = d_1 \times \left(\frac{40}{d_1}\right) \) to find your diagonals and calculate the area. Don't forget, the height of the rhombus can then be calculated by using the area formula \( \text{Area} = \text{base} \times \text{height} \).