Assuming you have a GTF/GFF file, something like the following in R will work. This also computes the GC content of each gene, so you can simplify things from this example rather considerably. The important part is split(), which breaks things up be gene, followed by reduce(), which merges overlapping exons such that you don't double count anything. After that, it's just a matter of lapply()ing a function to sum() the width (which I actually did in a redundant way below).

N.B., you'll obviously need to change the GTFfile and FASTAfile definitions as well.

#!/usr/bin/env Rscript
library(GenomicRanges)
library(rtracklayer)
library(Rsamtools)

GTFfile = "~/Documents/Misc/Mus_musculus/Ensembl/GRCm38.71/Annotation/Mus_musculus.GRCm38.71.gtf"
FASTAfile = "~/Documents/Misc/Mus_musculus/Ensembl/GRCm38.71/Sequence/Mus_musculus.GRCm38.71.fa"

#Load the annotation and reduce it
GTF <- import.gff(GTFfile, format="gtf", genome="GRCm38.71", asRangedData=F, feature.type="exon")
grl <- reduce(split(GTF, elementMetadata(GTF)$gene_id))
reducedGTF <- unlist(grl, use.names=T)
elementMetadata(reducedGTF)$gene_id <- rep(names(grl), elementLengths(grl))

#Open the fasta file
FASTA <- FaFile(FASTAfile)
open(FASTA)

#Add the GC numbers
elementMetadata(reducedGTF)$nGCs <- letterFrequency(getSeq(FASTA, reducedGTF), "GC")[,1]
elementMetadata(reducedGTF)$widths <- width(reducedGTF)

#Create a list of the ensembl_id/GC/length
calc_GC_length <- function(x) {
    nGCs = sum(elementMetadata(x)$nGCs)
    width = sum(elementMetadata(x)$widths)
    c(width, nGCs/width)
}
output <- t(sapply(split(reducedGTF, elementMetadata(reducedGTF)$gene_id), calc_GC_length))
colnames(output) <- c("Length", "GC")

write.table(output, file="GC_lengths.tsv", sep="\t")

Since genes may have multiple transcripts, I would merge all transcripts into one transcript for the same gene.

If you use R, you can do like this: For each gene, save positions of exons from different transcripts as a list of GRanges/IRanges objects and do union operation.

And finally use the length of these merged exons.