This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Morning black — let's get this done. To find the area of the shaded part, we will calculate the total area of the rectangle PQRS and then subtract the areas of the three unshaded triangles. Step 1: Calculate the area of the rectangle PQRS. The length of the rectangle PQ is 16 cm. The width of the rectangle PS is 10 cm. Area of rectangle PQRS = length × width Area of rectangle PQRS = 16 cm × 10 cm = 160 cm^2 Step 2: Calculate the areas of the three unshaded triangles. The unshaded triangles are PQX, QRY, and SXY. Area of PQX: This is a right-angled triangle at P. Base PQ = 16 cm. Height PX = 4 cm. Area( PQX) = (1)/(2) × base × height = (1)/(2) × 16 cm × 4 cm = 32 cm^2 Area of QRY: This is a right-angled triangle at R. Base YR = 4 cm. Height QR = 10 cm. Area( QRY) = (1)/(2) × base × height = (1)/(2) × 4 cm × 10 cm = 20 cm^2 Area of SXY: This is a right-angled triangle at S. First, find the lengths of SX and SY. SX = PS - PX = 10 cm - 4 cm = 6 cm. SY = SR - YR = 16 cm - 4 cm = 12 cm. Area( SXY) = (1)/(2) × base × height = (1)/(2) × 6 cm × 12 cm = 36 cm^2 Step 3: Calculate the total area of the unshaded parts. Total unshaded area = Area( PQX) + Area( QRY) + Area( SXY) Total unshaded area = 32 cm^2 + 20 cm^2 + 36 cm^2 = 88 cm^2 Step 4: Calculate the area of the shaded part. Area of shaded part = Area of rectangle PQRS - Total unshaded area Area of shaded part = 160 cm^2 - 88 cm^2 = 72 cm^2 The area of the shaded part is 72 cm^2. Send me the