A thin metal plate is cut in the shape of the ellipse x²/49 + y²/25 = 1, where x and y are in…

Step 1. The semi-axes. $a^2 = 49$ gives $a = 7$ centimetres, and $b^2 = 25$ gives $b = 5$ centimetres.

Step 2. The area. $\pi ab = 35\pi \approx 109.96$ square centimetres. This comes from four times the quarter, $4 \times \dfrac{b}{a}\displaystyle\int_0^a \sqrt{a^2 - x^2}\,dx$.

Step 3. The mass. $0.8\ \text{g/cm}^2 \times 35\pi\ \text{cm}^2 = 28\pi \approx 87.96$ grams.