Calculate the semi-perimeter s.

Here are the solutions to the problems. 1. Find the area of the triangle with sides 8m, 9m, and 15m. Step 1: Calculate the semi-perimeter s. The semi-perimeter s is half the sum of the side lengths a, b, c. s = (a+b+c)/(2) = (8+9+15)/(2) = (32)/(2) = 16 m Step 2: Apply Heron's formula for the area of a triangle. The area A is given by A = sqrt(s(s-a)(s-b)(s-c)). A = sqrt(16(16-8)(16-9)(16-15)) A = sqrt(16 × 8 × 7 × 1) A = sqrt(896) A ≈ 29.933 m^2 Rounding to one decimal place: The area of the triangle is 29.9 m^2. 2. Find the area of the parallelogram with sides 9cm and 12cm, and an angle of 48^ between them. Step 1: Use the formula for the area of a parallelogram. The area A of a parallelogram with sides a and b and angle between them is A = ab . A = 9 cm × 12 cm × 48^ A = 108 × 48^ Step 2: Calculate the value. Using 48^ ≈ 0.74314: A = 108 × 0.74314 A ≈ 80.259 cm^2 Rounding to two decimal places: The area of the parallelogram is 80.26 cm^2. 3. Find the area of triangle PQR with PQ = 7.5, PR = 8.3, and P = 56^. Step 1: Use the formula for the area of a triangle given two sides and the included angle. The area A is given by A = (1)/(2) PQ × PR × P. A = (1)/(2) × 7.5 × 8.3 × 56^ Step 2: Calculate the value. A = (1)/(2) × 62.25 × 56^ Using 56^ ≈ 0.82904: A = 31.125 × 0.82904 A ≈ 25.804 Rounding to two decimal places: The area of triangle PQR is 25.80. 4. Calculate the capacity in litres of a container that measures 2m by 1.5m by 1.2m. Step 1: Calculate the volume of the container in cubic meters. The volume V of a rectangular container is V = length × width × height. V = 2 m × 1.5 m × 1.2 m V = 3.6 m^3 Step 2: Convert the volume from cubic meters to litres. Since 1 m^3 = 1000 litres: Capacity = 3.6 m^3 × 1000 litres/m^3 Capacity = 3600 litres The capacity of the container is 3600 litres. 5. Solve the ratio problems. a) Increase 200 in ratio 5:4. Step 1: Multiply the original value by the given ratio. To increase in the ratio 5:4, the new value is (5)/(4) of the original value. New value = (5)/(4) × 200 New value = 5 × (200)/(4) New value = 5 × 50 New value = 250 The increased value is 250. b) Decrease 480 in ratio 5:8. Step 1: Multiply the original value by the given ratio. To decrease in the ratio 5:8, the new value is (5)/(8) of the original value. New value = (5)/(8) × 480 New value = 5 × (480)/(8) New value = 5 × 60 New value = 300 The decreased value is 300. Last free one today — make it count tomorrow, or type /upgrade for unlimited.