This paper presents a summarization technique for text documents exploiting the semantic similarity between sentences to remove the redundancy from the text. Semantic similarity scores are computed by mapping the sentences on a semantic space using Random Indexing. Random Indexing, in comparison with other semantic space algorithms, presents a computationally efficient way of implicit dimensionality reduction. It involves inexpensive vector computations such as addition. It thus provides an efficient way to compute similarities between words, sentences and documents. Random Indexing has been used to compute the semantic similarity scores of sentences and graph-based ranking algorithms have been employed to produce an extract of the given text.