Melanoma is an aggressive form of skin cancer, where survival rates are high when caught early. Breslow thickness is a measure of the depth of tumor into the skin, which provides a metric on how far the melanoma has metastasized into the deeper regions of the skin. Traditionally, the Breslow thickness measurement is used to determine the stage and severity of melanoma even though it does not take into account cross-sectional area, which has been shown to be more useful for prognostic and treatment purposes. We propose to use computer vision based methods to estimate cross-sectional area of invasive melanoma by segmenting it out in whole-slide images (WSIs) from microscopes. We present two transformer-based methods to segment invasive melanoma. First, we design a custom segmentation model from a transformer backbone for classification pretrained on breast cancer WSIs, and adapt the architecture accordingly to perform melanoma segmentation. In our second approach, we utilize a segmentation backbone pretrained on natural images and finetune it for the melanoma segmentation task. Both proposed approaches outperform existing work in terms of mean intersection over union by up to 9% and 12% respectively, while also being more memory efficient and easier to train. Analysis of our segmentation results from a board-certified dermatologist reveals that our models perform well compared to the trained human eye.